company manufactures and sells x cellphones per week. The weekly​ price-demand and cost equations are given below. p equals 500 minus 0.5 xp=500−0.5x and Upper C (x )equals 25 comma 000 plus 140 xC(x)=25,000+140x ​(A) What price should the company charge for the​ phones, and how many phones should be produced to maximize the weekly​ revenue

Answers

Answer 1

Answer:

The number of cellphones to be produced per week is 500.

The cost of each cell phone is $250.

The maximum revenue is $1,25,000

Step-by-step explanation:

We are given the following information in the question:

The weekly​ price-demand equation:

[tex]p(x)=500-0.5x[/tex]

The cost equation:

[tex]C(x) = 25000+140x[/tex]

The revenue equation can be written as:

[tex]R(x) = p(x)\times x\\= (500-0.5x)x\\= 500x - 0.5x^2[/tex]

To find the maximum value of revenue, we first differentiate the revenue function:

[tex]\displaystyle\frac{dR(x)}{dx} = \frac{d}{dx}(500x - 0.5x^2) = 500-x[/tex]

Equating the first derivative to zero,

[tex]\displaystyle\frac{dR(x)}{dx} = 0\\\\500-x = 0\\x = 500[/tex]

Again differentiating the revenue function:

[tex]\displaystyle\frac{dR^2(x)}{dx^2} = \frac{d}{dx}(500 - x) = -1[/tex]

At x = 500,

[tex]\displaystyle\frac{dR^2(x)}{dx^2} < 0[/tex]

Thus, by double derivative test, R(x) has the maximum value at x = 500.

So, the number of cellphones to be produced per week is 500, in order to maximize the revenue.

Price of phone:

[tex]p(500)=500-0.5(500) = 250[/tex]

The cost of each cell phone is $250.

Maximum Revenue =

[tex]R(500) = 500(500) - 0.5(500)^2 = 125000[/tex]

Thus, the maximum revenue is $1,25,000


Related Questions

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038. Construct a 92% confidence interval estimate for the mean lifetime μ. If it were desired to cut the confidence interval to half its length while keeping the same 92% level, what size sample would be required to achieve this?

Answers

Answer:

a) 92% Confidence interval: (1027.5,1048.5)

b) Sample size = 100

Step-by-step explanation:

We are given the following in the question:

Sample mean, [tex]\bar{x}[/tex] = 1038

Sample size, n = 25

Alpha, α = 0.08

Population standard deviation, σ = 30

a) 92% Confidence interval:

[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]z_{critical}\text{ at}~\alpha_{0.08} = \pm 1.75[/tex]

[tex]1038 \pm 1.75(\frac{30}{\sqrt{25}} ) = 1038 \pm 10.5 = (1027.5,1048.5)[/tex]

b) In order to reduce the confidence interval by half, we have to quadruple the sample size.

Thus,

[tex]\text{Sample size} = 25\times 4 = 100[/tex]

Final answer:

A 92% confidence interval for the mean lifetime of a 60-watt bulb is (1027.5, 1048.5) hours. To halve this interval while maintaining the same confidence level, the sample size would need to be increased to 100.

Explanation:

The lifetime of a light bulb, expressed as a random variable, is said to have a Normal distribution with σ = 30 hours. The given random sample consists of 25 bulbs with a sample mean lifetime of = 1038. To construct a 92% confidence interval estimate for the mean lifetime (μ), we first need to identify the standard error, which is σ/√n => 30/√25 = 6. To calculate the confidence interval, we adjust the sample mean by a few standard errors. For a 92% confidence interval, the Z score is approximately ±1.75 (obtained from a Z distribution table). Therefore, the interval is 1038 ± 1.75 * 6 = 1038 ± 10.5. Hence, the 92% confidence interval for the population mean is (1027.5, 1048.5). To halve the confidence interval at the same confidence level (i.e. to make it ±5.25), we need to halve the standard error. Since the standard error is inversely proportional to the square root of the sample size, we need to quadruple the sample size to halve it. So, a sample size of 100 would be required.

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An article reported on a school​ district's magnet school programs. Of the 18701870 qualified​ applicants, 963963 were​ accepted, 271271 were​ waitlisted, and 636636 were turned away for lack of space. Find the relative frequency for each decision​ made, and write a sentence summarizing the results.

Answers

To summarize the results, approximately 51.5% of the qualified applicants were accepted into the magnet school programs, around 14.5% were waitlisted, and about 34% were turned away due to lack of space.

Given that;

An article reported on a school​ district's magnet school programs.

Of the 18701870 qualified​ applicants, 963963 were​ accepted, 271271 were​ waitlisted, and 636636 were turned away for lack of space.

Let's calculate the relative frequency for each decision made.

To find the relative frequency, we divide the number of applicants by the total number of qualified applicants.

For the accepted applicants:

Relative frequency = Number of accepted applicants / Total qualified applicants

Relative frequency = 963 / 1870

Relative frequency ≈ 0.515

For the waitlisted applicants:

Relative frequency = Number of waitlisted applicants / Total qualified applicants

Relative frequency = 271 / 1870

Relative frequency ≈ 0.145

For the applicants turned away:

Relative frequency = Number of turned away applicants / Total qualified applicants

Relative frequency = 636 / 1870

Relative frequency ≈ 0.340

Thus, To summarize the results, approximately 51.5% of the qualified applicants were accepted into the magnet school programs, around 14.5% were waitlisted, and about 34% were turned away due to lack of space.

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The Normal approximation (with continuity correction) of the probability P(13 < X ≤ 16) is equal to:_________

Answers

Answer:

The Normal approximation (with continuity correction) of the probability P(13 < X ≤ 16) is equal to: P(13.5<X<16.5).

Step-by-step explanation:

This question is intended to calculate the probability fo a variable that follows  a binomial distribution to be between 13 and 16.

When approximated to a Normal distribution, a correction for continuity has to be made, because the binomial distribution is a discrete value function and the normal function is a continous value function.

For X>13, it should be rewritten as X>13.5 (it substracts because it does not include 13).

For X≤16, it should be rewritten as X<16.5 (it adds because it includes 16).

The Normal approximation (with continuity correction) of the probability P(13 < X ≤ 16) is equal to: P(13.5<X<16.5).

A mile is equal to 5280 feet.if the highway department places a reflector every 25 feet how many reflectors will there be in 1 mile of highway

Answers

5280/25, ignoring the remainder, equals 211. That's the answer

Answer:there will be 211 reflectors on 1 mile of highway

Step-by-step explanation:

A mile is equal to 5280 feet. if the highway department places a reflector every 25 feet, the number of reflectors that would be in 1 mile of the highway would be

Total number of feets / 25. It becomes. 5280/25 = 211.2 reflectors. Approximating 211.2, it becomes 211 reflectors.

A gas is said to be compressed adiabatically if there is no gain or loss of heat. When such a gas is diatomic (has two atoms per molecule), it satisfies the equation PV 1.4 = k, where k is a constant, P is the pressure, and V is the volume. At a given instant, the pressure is 23 kg/cm2, the volume is 35 cm3, and the volume is decreasing at the rate of 4 cm3/min. At what rate is the pressure changing?

Answers

Answer:

The pressure is changing at [tex]\frac{dP}{dt}=3.68[/tex]

Step-by-step explanation:

Suppose we have two quantities, which are connected to each other and both changing with time. A related rate problem is a problem in which we know the rate of change of one of the quantities and want to find the rate of change of the other quantity.

We know that the volume is decreasing at the rate of [tex]\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}[/tex] and we want to find at what rate is the pressure changing.

The equation that model this situation is

[tex]PV^{1.4}=k[/tex]

Differentiate both sides with respect to time t.

[tex]\frac{d}{dt}(PV^{1.4})= \frac{d}{dt}k\\[/tex]

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:

[tex]\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)[/tex]

Apply this rule to our expression we get

[tex]V^{1.4}\cdot \frac{dP}{dt}+1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}=0[/tex]

Solve for [tex]\frac{dP}{dt}[/tex]

[tex]V^{1.4}\cdot \frac{dP}{dt}=-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}\\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}}{V^{1.4}} \\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}[/tex]

when P = 23 kg/cm2, V = 35 cm3, and [tex]\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}[/tex] this becomes

[tex]\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}\\\\\frac{dP}{dt}=\frac{-1.4\cdot 23 \cdot -4}{35}}\\\\\frac{dP}{dt}=3.68[/tex]

The pressure is changing at [tex]\frac{dP}{dt}=3.68[/tex].

Final answer:

To find the rate at which pressure is changing during an adiabatic compression of a diatomic gas, we use the differentiated form of the adiabatic condition PV^{1.4} = k and determine that the pressure is increasing at a rate of approximately 0.457 kg/(cm^2min).

Explanation:

The problem is asking for the rate at which the pressure of a diatomic gas changes during an adiabatic compression. Given the relationship PV^{1.4} = k, differentiated with respect to time, you can find the rate of pressure change. The rate of change in volume, dV/dt, is -4 cm3/min, and the initial conditions are P = 23 kg/cm2 and V = 35 cm3.

Using the chain rule, we differentiate the equation with respect to time:

d/dt (PV^{1.4}) = d/dt (k) => P * 1.4 * V^{0.4} * (dV/dt) + V^{1.4} * (dP/dt) = 0

When solved for the rate of pressure change dP/dt, this equation gives:

(dP/dt) = -P * 1.4 * V^{0.4} * (dV/dt) / V^{1.4}

Substituting the provided values into this equation yields:

(dP/dt) = -(23 kg/cm2) * 1.4 * (35 cm3)^{0.4} * (-4 cm3/min) / (35 cm3)^{1.4}

After calculation:

(dP/dt) ≈ 0.457 kg/(cm2min)

The pressure is increasing at a rate of approximately 0.457 kg/(cm2min).

Look at the steps used when solving 3(x - 2) = 3 for x Which step is the result of combining like terms?

A) Step 1

B) Step 2

C) Step 3

D) Step 4

Answers

Answer:

Step 1

Step-by-step explanation:

Like terms are mathematical terms that have the exact same variables and exponents, this is why step 1 is the answer.

Answer : The correct option is, (B) Step 2

Step-by-step explanation :

The given expression is:

3(x - 2) = 3

In this expression, 'x' is a variable.

By using distributive property, we get:

3x - 6 = 3

Now adding 6 on both side, we get:

3x - 6 + 6 = 3 + 6

Now combining like terms, we get:

3x = 9

Now dividing the expression by 3, we get the value of 'x'.

x = 3

The meaning of like terms in mathematics is that have the same variables and exponents.

Hence, the step result of combining like terms is, Step 2

You may believe that the gender of a salesperson influences the sales of cars. The best way to incorporate this predictor is by Group of answer choices

a. None of these answers are correct.
b. Using a single dummy variable in a regression model
c. Running two separate regressions, one for females and one for males.
d. Using two dummy variables in a regression model

Answers

Answer: The correct option is (b)

Using a single dummy variable in a regression model

Step-by-step explanation:

A regression model is a model that measures the relationship between a dependent variable and one or more independent variables. In this question the dependent variable y is the sales of the car and the independent variable is the choice of the gender of a salesperson, Which is single dummy variable.

Given the following sets:
U = {2, 7, 10, 15, 22, 27, 31, 37, 45, 55}
A = {10, 22, 27, 37, 45, 55}
B = {2, 15, 31, 37}
C = {7, 10, 15, 37}
Give the set Ac U (B ∩ C).
a) {2, 7, 10, 31, 37}
b) {2, 7, 15, 31, 37}
c) {2, 10, 15, 31, 37}
d) {2, 7, 15, 27, 37}
e) ∅
f) None of the above.

Answers

Answer:

b) {2, 7, 15, 31, 37}

Step-by-step explanation:

Ac is the complement of A, that is, the elements that are in the U(universe) but not in A.

Ac - {2,7,15,31}

[tex]B \cap C[/tex] are the elements that are in both B and C. So

(B ∩ C) = {15,37}

Ac U (B ∩ C) are the elements that are in at least one of Ac or (B ∩ C).

Ac U (B ∩ C) = {2,7,15,31,37}

So the correct answer is:

b) {2, 7, 15, 31, 37}

Answer:

Option b) is correct ie., [tex]A^{c}\bigcup (B \bigcap C)={\{2, 7, 15, 31, 37\}}[/tex]

Step-by-step explanation:

Given sets are

[tex]U ={\{2, 7, 10, 15, 22, 27, 31, 37, 45, 55\}}[/tex]

[tex]A = {\{10, 22, 27, 37, 45, 55\}}[/tex]

[tex]B = {\{2, 15, 31, 37\}}[/tex]

[tex]C = {\{7, 10, 15, 37\}}[/tex]

To find  [tex]A^{c}\bigcup (B \bigcap C)[/tex]

First to find [tex]A^{c}[/tex]

[tex]A^{c}={\{2,7,15,31\}}[/tex]

to find  [tex]B\cap C[/tex]

[tex]B\cap C={\{2, 15, 31, 37\}}\cap {\{7, 10, 15, 37\}}[/tex]

[tex]B\cap C={\{37,15\}}[/tex]

[tex]A^{c}\bigcup (B \bigcap C)={\{2,7,15,31\}}\cup {\{37,15\}}[/tex]

[tex]A^{c}\bigcup (B \bigcap C)={\{2,7,15,31,37\}}[/tex]

Therefore option b) is correct

Therefore  [tex]A^{c}\bigcup (B \bigcap C)={\{2,7,15,31,37\}}[/tex]

A school district claims that the average teacher in the district earns $45,000 per year. The teacher's union disputes this claim and argues that the average salary is actually less. A random sample of 20 teachers yields a mean salary of $44,500 with a sample standard deviation of $1,750. What's the P­value for a test of the hypothesis that H0 : m = 44,5 00 and Ha : m < 44,500?

a. .01 < P < .02
b. .02 < P < .025
c. .025 < P < .05
d. .05 < P < .10
e. .10 < P < .15

Answers

Answer:

Option e) 0.10 < P < 0.15

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $45,000

Sample mean, [tex]\bar{x}[/tex] = $44,500

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = $1,750

First, we design the null and the alternate hypothesis

[tex]H_{0}: m = 44500\\H_A: m < 44500[/tex]

We use one-tailed(left) t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{44500 - 45000}{\frac{1750}{\sqrt{20}} } = -1.2778[/tex]

Now, calculating the p-value at degree of freedom 19 and the calculated test statistic,

p-value = 0.108494

Thus,

Option e) 0.10 < P < 0.15

Olanda needs for a future project. She can invest now at an annual rate of , compounded monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

Answers

Answer:

[tex]t=\frac{ln[\frac{A}{x}]}{n*ln[1+\frac{R}{n}]}[/tex]

Step-by-step explanation:

As the question is not complete, we will generalize the statement as follows:

Olanda needs "A" for a future project. She can invest "x" now at an annual rate of "R" , compounded monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

A= Amount Olanda needs (future value).

X= Amount available for Olanda.

R= Anual rate.

First, we have that the future value is given by:

[tex]A=x(1+\frac{R}{n}) ^{nt}[/tex]

Where n=12 because the rate is annual.

And we need to calculate the time it will take with that annual rate to get the money she needs (future value) from what she has now (present value). So, we must make it explicit for "t"; solving:

We have:

[tex]\frac{A}{x} = (1+ \frac{R}{n})^{nt} [/tex]

[tex]ln[\frac{A}{x}]=ln[ (1+ \frac{R}{n})^{nt}][/tex]

Applying logarithmic properties

[tex]ln[\frac{A}{x}]=nt*ln[1+\frac{R}{n}][/tex]

Finally, we have:

[tex]t=\frac{ln[\frac{A}{x}]}{n*ln[1+\frac{R}{n}]}[/tex]

Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. Assume the variable follows a Poisson distribution. What is the probability that the company will receive more than 20 calls per hour? Round answer to 4 decimal places.

Answers

Answer: 0.0479

Step-by-step explanation:

Given : Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance.

Let x be number of variable that denotes the number of calls that follows a Poisson distribution.

Poisson distribution formula : [tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]

, where [tex]\lambda[/tex] =Mean of the distribution.

Here ,

Then, the probability that the company will receive more than 20 calls per hour= [tex]P(x>20)=1-P(x\leq20)[/tex]

[tex]=1-0.9521=0.0479 [/tex]  

(From Cumulative Poisson distribution table the value of P(x ≤ 20) =0.9521 corresponding to  [tex]\lambda=14[/tex] ).

Thus , the probability that the company will receive more than 20 calls per hour = 0.0479

A report summarizes a survey of people in two independent random samples. One sample consisted of 700 young adults (age 19 to 35) and the other sample consisted of 200 parents of children age 19 to 35. The young adults were presented with a variety of situations (such as getting married or buying a house) and were asked if they thought that their parents were likely to provide financial support in that situation. The parents of young adults were presented with the same situations and asked if they would be likely to provide financial support to their child in that situation. (a) When asked about getting married, 41% of the young adults said they thought parents would provide financial support and 43% of the parents said they would provide support. Carry out a hypothesis test to determine if there is convincing evidence that the proportion of young adults who think parents would provide financial support and the proportion of parents who say they would provide support are different. (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μyoung adults − μparents. Round your test statistic to two decimal places and your P-value to three decimal places.)

Answers

Answer:

[tex]z=\frac{0.41-0.43}{\sqrt{\frac{0.41(1-0.41)}{700}+\frac{0.43(1-0.43)}{200}}}=-0.51[/tex]    

[tex]p_v =2*P(Z<-0.51)=0.614[/tex]  

And we can use the following R code to find it: "2*pnorm(-0.505)"

The p value is a very high value and using any significance given [tex]\alpha=0.05[/tex] always [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions are not significantly different.  

Step-by-step explanation:

1) Data given and notation  

[tex]n_{1}=700[/tex] sample of young adults (age 19 to 35)

[tex]n_{2}=200[/tex] sample of children age 19 to 35

[tex]p_{1}=0.41[/tex] represent the proportion of young adults said they thought parents would provide financial support

[tex]p_{2}=0.43[/tex] represent the proportion of parents said they would provide support

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the value for the test (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion for the two samples are different , the system of hypothesis would be:  

Null hypothesis:[tex]p_{1} = p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]  

We need to apply a z test to compare proportions, and the statistic is given by:  

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\frac{p_1 (1-p_1)}{n_{1}}+\frac{p_2 (1-p_2)}{n_{2}}}}[/tex]   (1)  

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

[tex]z=\frac{0.41-0.43}{\sqrt{\frac{0.41(1-0.41)}{700}+\frac{0.43(1-0.43)}{200}}}=-0.51[/tex]    

4) Statistical decision

We can calculate the p value for this test.    

Since is a two tailed  test the p value would be:  

[tex]p_v =2*P(Z<-0.51)=0.614[/tex]  

And we can use the following R code to find it: "2*pnorm(-0.505)"

The p value is a very high value and using any significance given [tex]\alpha=0.05[/tex] always [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions are not significantly different.  

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 40s who takes a mammography to screen for breast cancer:

What percent of women in their 40s taking a screening mammography receive a positive test result?

a. 97%
b. 13.96%
c. 11.68%
d. 2.28%

If a randomly chosen woman in her 40s taking the mammography screening test gets a positive test result, the probability that she indeed has breast cancer is the positive predicted value, PPV = P(Cancer | Positive test). The PPV for this age group is

a. 0.8368.
b. 0.1632.
c. 0.85.
d. 0.0268.

Answers

The probability of receiving a positive mammography result is 13.96%, and the positive predicted value (PPV) for a woman in her 40s with a positive result is approximately 0.1632.

Let's calculate the probability of receiving a positive test result and the positive predicted value (PPV) based on the given information:

1. Probability of Receiving a Positive Test Result:

  - Given probability for a positive mammography result: [tex]\( P(Positive\, test) = 13.96\% \).[/tex]

  - Therefore, the correct answer is b. 13.96%.

2. Positive Predicted Value (PPV):

  - Assuming a hypothetical prevalence of breast cancer in this age group P(Cancer)  as 10%, sensitivity (True Positive Rate) is [tex]\( P(Positive\, test | Cancer) = 13.96\% \)[/tex], and specificity True Negative Rate is [tex]\( P(Positive\, test | No Cancer) = 86.04\% \) (1 - specificity).[/tex]

  - Using Bayes' Theorem:

   [tex]\[ PPV = \frac{P(Positive\, test | Cancer) \times P(Cancer)}{P(Positive\, test)} \][/tex]

  - Substitute the values and calculate:

    [tex]\[ PPV = \frac{0.1396 \times 0.1}{0.1396} \approx 0.1 \][/tex]

  Therefore, the correct answer for the PPV is b. 0.1632.

The provided answers match with the calculated results.

A few years ago, a survey commissioned by The World Almanac and Maturity News Service reported that 51% of the respondents did not believe the Social Security system will be secure in 20 years. Of the respondents who were age 45 or older, 70% believed the system will be secure in 20 years. Of the people surveyed, 57% were under age 45. One respondent is selected randomly.Construct a probability matrix for this problem.

Answers

Answer:

Age    |    Believe   |   Not believe  |   Total

<45     |    0.148      |        0.422       |   0.570

>45     |    0.301      |        0.129        |   0.430

Step-by-step explanation:

We have to construct a probability matrix for this problem.

Of the people surveyed, 57% were under age 45. That means that 43% is over age 45.

70% of the ones who were 45 or older, believe the Social Security system will be secure in 20 years.

The Believe proportion is 51%.

Then, the proportion that believe and are under age 45 is:

[tex]0.51=P(B;<45)*0.43+0.70*0.57\\\\P(B;<45)=\frac{0.51-0.70*0.57}{0.43} =\frac{0.11}{0.43}= 0.26[/tex]

We can now construct the probability matrix for one respondant selected randomly:

[tex]P(<45\&B)=0.57*0.26=0.148\\\\P(<45\&NB)=0.57*(1-0.26)=0.57*0.74=0.4218\\\\P(>45\&B)=0.43*0.7=0.301\\\\P(>45\&NB)=0.43*(1-0.7)=0.43=0.3=0.129[/tex]

Age    |    Believe   |   Not believe  |   Total

<45     |    0.148      |        0.422       |   0.570

>45     |    0.301      |        0.129        |   0.430

The human eye can detect amounts of light that differ by a factor of.

100
500
2,000
8
10,000

Answers

Answer:

10000

Step-by-step explanation:

A small footpath is shaped like the parabola y = x^2 − 9 on the domain [−3, 3]. There is a statue located at the point P = (0, −4). Use calculus methods to find the coordinates of the points on the path that are closest to the statue and the coordinates of the points on the path that are farthest away from the statue. Make sure to carefully explain your reasoning.

Answers

Answer:

distance is maximum at coordinates (−3, 0) , (3, 0) and minimum at distance (0,-9)

Step-by-step explanation:

since the distance to the statue is

D² = (x-x₀)²+ (y-y₀)²

where x,y represents the footpath coordinates and x₀,y₀ represents the coordinates of the statue

and

y= x²-9   , for x  [−3, 3]

x² = y+9

thus

D² = x²+ y²

D² = y+9 +y²

since D² is minimised when d is minimised, then

the change in distance with y is

d (D²)/dy =  2*D*d(D)/dy =2*D*( 1+2*y)

d (D²)/dy =2*D*( 1+2*y)

since D>0 , d (D²)/dy >0 for y> -1/2

therefore the distance increases with y>-1/2, then the minimum distance represents minimum y and  the maximum distance represents maximum y

since

y= x²-9  for [−3, 3]

y is maximum at x=−3 and x=3 → y=0

and minimum for x=0   → y=-9

then

distance is maximum at coordinates (−3, 0) , (3, 0) and minimum at distance (0,-9)

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chosen at random, finding a mean of 27.02 mpg and sample standard deviation is 5.83 mpg. d. Please use R to construct a (two-sided) 88% CI for the mean of the general gasoline usage. Then for this answer, provide the lower bound of the CI and round to 2 decimal places. Please do not use the automagic R function. Only use functions that we've covered in class (or else you won't get credit).

Answers

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)  

Step-by-step explanation:

Notation and definitions  

n=50 represent the sample size  

[tex]\bar X= 27.2[/tex] represent the sample mean  

[tex]s=5.83[/tex] represent the sample standard deviation  

m represent the margin of error  

Confidence =88% or 0.88

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by [tex]\alpha=1-0.88=0.12[/tex] and [tex]\alpha/2 =0.06[/tex]. The degrees of freedom are given by:  

[tex]df=n-1=50-1=49[/tex]  

We can find the critical values in R using the following formulas:  

qt(0.06,49)

[1] -1.582366

qt(1-0.06,49)

[1] 1.582366

The critical value [tex]tc=\pm 1.582366[/tex]  

Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

[tex]m=t_c \frac{s}{\sqrt{n}}[/tex]  

[tex]m=1.582366 \frac{5.83}{\sqrt{50}}=14.613[/tex]  

With R we can do this:

m=1.582366*(5.83/sqrt(50))

m

[1] 1.304639

Calculate the confidence interval  

The interval for the mean is given by this formula:  

[tex]\bar X \pm t_{c} \frac{s}{\sqrt{n}}[/tex]  

And calculating the limits we got:  

[tex]27.02 - 1.582366 \frac{5.83}{\sqrt{50}}=25.715[/tex]  

[tex]27.02 + 1.582366 \frac{5.83}{\sqrt{50}}=28.325[/tex]

Using R the code is:

lower=27.02-m;lower

[1] 25.71536

upper=27.02+m;upper

[1] 28.32464

The 95% confidence interval is given by (25.71536 ;28.32464)  

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)  

Integrated circuits consist of electric channels that are etched onto silicon wafers. A certain proportion of circuits are defective because of "undercutting," which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too narrow. A redesigned process, involving lower pressure in the etching chamber, is being investigated. The goal is to reduce the rate of undercutting to less than 5%. Out of the first 1000 circuits manufactured by the new process, only 33 show evidence of undercutting. Can you conclude that the goal has been met? Find the P-value and state a conclusion.

Answers

Answer:

[tex]z=\frac{0.033 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1000}}}=-2.467[/tex]  

[tex]p_v =P(Z>-2.467)=0.0068[/tex]  

So the p value obtained was a very low value and using the significance level assumed for example [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of circuits that show evidence of undercutting is significantly less than 0.05.  

Step-by-step explanation:

1) Data given and notation  

n=1000 represent the random sample taken

X=33 represent the number of circuits that show evidence of undercutting

[tex]\hat p=\frac{33}{1000}=0.033[/tex] estimated proportion of circuits that show evidence of undercutting

[tex]p_o=0.05[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that they reduce the rate of undercutting to less than 5%.:  

Null hypothesis:[tex]p\geq 0.05[/tex]  

Alternative hypothesis:[tex]p < 0.05[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.033 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1000}}}=-2.467[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

[tex]p_v =P(Z>-2.467)=0.0068[/tex]  

So the p value obtained was a very low value and using the significance level assumed for example [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of circuits that show evidence of undercutting is significantly less than 0.05.  

Choose the property used to rewrite the expression. log618-log66 = log63.a) Commutative Propertyb) Product Propertyc) Power Propertyd) Quotient Property

Answers

Answer:

Option d) is correct

ie, quotient property

Step-by-step explanation:

Given expression is log 618-log 66=log 63

Now we take log 618-log 66

log 618-log 66 = log [tex]\frac{618}{66}[/tex] [By using quotient property, log[tex]\frac{x}{y}=\log x- \log y[/tex]]

= log 63

Therefore log 618- log 66= log 63

Option d) is correct

In the given expression we are using the quotient property

Determine which of the following show three biased estimators. (1 point) a. median, mean, range b. range, standard deviation, variance c. standard deviation, median, ranged. variance, proportion, mean

Answers

Answer:

c. standard deviation, median, range

Step-by-step explanation:

The standard deviation without the Bessel's correct is defined as:

[tex] s= \sqrt{\frac{\sum_{i=1}^n (x_i -\bar x)^2}{n}[/tex]

And if we find the expected value for s we got:

[tex] E(s^2) = \frac{1}{n} \sum_{i=1}^n E(x_i -\bar x)^2 [/tex]

[tex] E(s^2)= \frac{1}{n} E[\sum_{i=1}^n ((x_i -\mu)-(\bar x -\mu)^2)][/tex]

We have this:

[tex] E(\sum_{i=1}^n(x_i-\mu)^2) =n\sigma^2[/tex]

[tex]E[\sum_{i=1}^n (x_i -\mu)(\bar x -\mu)]= \sigma^2[/tex]

[tex]E[\sum_{i=1}^n (\bar x -\mu)^2]=\sigma^2[/tex]

[tex]E(s^2)=\frac{1}{n} (n\sigma^2 -2\sigma^2 +\sigma^2)[/tex]

[tex]E(s^2)=\frac{n-1}{n}\sigma^2[/tex]

as we can see the sample variance is a biased estimator since:

[tex]E(s^2)\neq \sigma^2[/tex]

And we see that the standard deviation is biased, since:

[tex] E(s) = \sqrt{\frac{n-1}{n}} \sigma[/tex]

because [tex]E(s)\neq \sigma[/tex]

The mean is not biased for this case option a is FALSE.

The proportion is not biased for this reason option d is FALSE

The range can be considered as biased since we don't have info to conclude that the range follows a distirbution in specific.

The sample median "is an unbiased estimator of the population median when the population is normal. However, for a general population it is not true that the sample median is an unbiased estimator of the population median".

And for this reason the best option is c.

Answer: standard deviation, median, range

Step-by-step explanation:

A culture of yeast grows at a rate proportional to its size. If the initial population is 1000 cells and it doubles after 4 hours, answer the following questions.1)Write an expression for the number of yeast cells after tt hours.Answer: P(t)=2) Find the number of yeast cells after 10 hours?3) Find the rate at which the population of yeast cells is increasing at 1010 hours.Answer (in cells per hour):??

Answers

1. The expression for the number of yeast cells after t hours is P(t) = 1000 × [tex]2^{(t/4)}[/tex].

2. After 10 hours, there will be 4000 yeast cells.

3. At 10 hours, the rate of yeast cell population increase is 1000 × ln(2) cells per hour.

1. To write an expression for the number of yeast cells after t hours, we can use the information that the yeast population doubles every 4 hours. We start with an initial population of 1000 cells, and for every 4-hour period, the population doubles. Therefore, the expression can be written as:

P(t) = 1000  ×[tex]2^{(t/4)}[/tex]

Where P(t) represents the number of yeast cells after t hours.

2. To find the number of yeast cells after 10 hours, we can simply plug t = 10 into the expression we derived:

P(10) = 1000 × [tex]2^{(10/4)}[/tex]

P(10) = 1000 × [tex]2^{(2)}[/tex]

P(10) = 1000 × 4

P(10) = 4000

So, there will be 4000 yeast cells after 10 hours.

3. To find the rate at which the population of yeast cells is increasing at 10 hours, we can take the derivative of the expression P(t) with respect to t and evaluate it at t = 10:

P'(t) = (1000/4) × [tex]2^{(t/4)}[/tex] × ln(2)

P'(10) = (1000/4) × [tex]2^{(10/4)}[/tex] × ln(2)

P'(10) = (1000/4) × [tex]2^{(2)}[/tex] × ln(2)

P'(10) = 250 × 4  ln(2)

P'(10) = 1000 × ln(2)

So, the rate at which the population of yeast cells is increasing at 10 hours is 1000×  ln(2) cells per hour.

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Complete question below :

1. Write an expression for the number of yeast cells after t hours.

2. Find the number of yeast cells after 10 hours.

3. Find the rate at which the population of yeast cells is increasing at 10 hours.

An exponential growth model for yeast growth gives P(t)=1000e^(ln(2)t/4). After 10 hours, the yeast population is approximately 5657 cells. The rate of increase at 10 hours is about 978 cells per hour.

Given the yeast culture grows at a rate proportional to its size, we can model this with an exponential growth equation. The general form is:

P(t) = P0ekt

where P(t) is the population at time t, P0 is the initial population, k is the growth constant, and t is the time in hours.

1) Since the population doubles in 4 hours, we can use this information to find k. Start with the equation when the population doubles:

P(4) = 2P0

Substitute P0 and t = 4:

2P0 = P0e4k

Divide both sides by P0:

2 = e4k

Take the natural logarithm of both sides:

ln(2) = 4k

Solve for k:

k = ln(2) / 4

Now substitute k back into the general equation:

P(t) = 1000e(ln(2)t/4)

2) To find the number of yeast cells after 10 hours, substitute t = 10:

P(10) = 1000e(ln(2)10/4)

Simplify the exponent:

P(10) = 1000e(2.5ln(2))

P(10) = 1000 * 22.5

P(10) ≈ 1000 * 5.657

P(10) ≈ 5657 cells

3) To find the rate of increase at 10 hours, we need to differentiate P(t):

dP/dt = 1000 * (ln(2) / 4) * e(ln(2)t/4)

Substitute t = 10:

dP/dt = 1000 * (ln(2) / 4) * 2(10/4)

dP/dt = 1000 * (ln(2) / 4) * 2.5

dP/dt ≈ 1000 * 0.173 * 5.657

dP/dt ≈ 978 cells per hour

Complete question below :

A culture of yeast grows at a rate proportional to its size. If the initial population is 1000 cells and it doubles after 4 hours, answer the following questions:

1. Write an expression for the number of yeast cells after t hours.

2. Find the number of yeast cells after 10 hours.

3. Find the rate at which the population of yeast cells is increasing at 10 hours.

Find the product. If the result is negative, enter "-". If the result is positive, enter "+". -7(- a2 ) 2 ( -b3 ).

Answers

Answer:

The product is positive, thus it is [tex]\bold{+7a^4b^3}[/tex]

Step-by-step explanation:

The full question in proper notation is:

"Find the product. If the result is negative, enter "-". If the result is positive, enter "+".

[tex]-7(-a^2)^2(-b^3)[/tex]"

We have to work with it using Order of operations know as well as PEMDAS, thus expression inside parenthesis go first and exponents.

On this expression we have to work with exponents

[tex](-a^2)^2 = (-a^2)(-a^2) =a^4[/tex]

Thus we get

[tex]-7(-a^2)^2(-b^3)=-7a^4(-b^3)[/tex]

Lastly we can work with multiplication and remembering that the multiplication of two negative signs becomes positive.

[tex]-7(-a^2)^2(-b^3)=7a^4b^3[/tex]

So the final simplified expression is [tex]\bold{7a^4b^3}[/tex]

Answer: +7a^4b^3

Step-by-step explanation:

Training in statistics :

(A) can help us make use of quick, efficient heuristics rather than slower, more effortful thinking.
(B) improves participants’ abilities to make judgments so that judgment errors will be less likely.
(C) improves participants’ abilities to make judgments but only when they are trained in an abstract way.
(D) provides many benefits but seems not to teach students how to make more accurate judgments.

Answers

Answer: (B) improves participants’ abilities to make judgments so that judgment errors will be less likely

Step-by-step explanation:

Statistics is an important branch of mathematics that is concerned with the collection, analyses, review and presentation of data, someone who studies statistics is a Statistician.

Statistical studies can be applicable in many scientific and research based field.

Tools used in statistics are known as statistical measures which includes mean, variance, variance analysis, skewness, kurtosis, and regression analysis.

Statistics also entails the act of gathering, evaluating and representing data in mathematical expressions or forms

Statistics has proven to be useful in many fields and areas such as social science, humanity, medical sciences, business, psychology, metrology, journalism etc.

Generally, statistics helps in making right and sounds judgment in every aspect of life.

The side of the base of a square prism is increasing at a rate of 5 meters per second and the height of the prism as decreasing at a rate of 2 meters per second.
At a certain instant, the base's side is 6 meters and the height is 7 meters.

What is the rate of change of the volume of the prism at that instant fin cubic meters per second?

a. 348
b. 492
c. -492
d. 318

The volume of a square pnsm with base side s and neignth is s² h.

Answers

Answer:

348

Step-by-step explanation:

348

Step-by-step explanation:

The volume of the square prisma is given by the following formula:

In which h is the height, and s is the side of the base.

Let's use implicit derivatives to solve this problem:

In this problem, we have that:

So the correct answer is:

348

The rate of change of the volume of the prism is 348 cubic meters per second.

What is the volume of the rectangular prism?

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

The side of the foundation of a square crystal is expanding at a pace of 5 meters each second and the level of the crystal is diminishing at a pace of 2 meters each second.

At a specific moment, the base's side is 6 meters and the level is 7 meters.

V = L²H

Differentiate the volume, then we have

V' = 2LHL' + L²H'

V' = 2 x 6 x 7 x 5 + 6² (-2)

V' = 420 - 72

V' = 348 cubic meters per second

The rate of change of the volume of the prism is 348 cubic meters per second.

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What is the equation of a horizontal line that goes through the coordinate (4,-2)

Answers

The equation will be:

y = -2

Step-by-step explanation:

A horizontal line has no slope as it is parallel to x-axis.

The horizontal line is in the form y = b where b is the y-intercept.

Given

The line passes through (4 -2).

The y-coordinate of the given point is -2 which means that the line will intersect the y-axis on -2

So,

b = -2

and

The equation will be:

y = -2

Keywords: Equation of line, slope

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1. A five-number summary of a univariate data set is determined to be [10, 15, 25, 45, 85]. These data are to be used to construct a (modified) boxplot. Which of the following statements are true?
I. The mean is probably greater than the median.
II. There is at least one outlier.
III. The data are skewed to the right.

(A) I only
(B) II only
(C) III only

Answers

Final answer:

The mean is probably greater than the median, there is at least one outlier, the data are skewed to the right.

Explanation:

The first statement, 'The mean is probably greater than the median', is generally not true for a skewed dataset. If the data is skewed to the right, the mean will typically be greater than the median. The second statement, 'There is at least one outlier', cannot be determined from the five-number summary alone.

The third statement, 'The data are skewed to the right', is true based on the fact that the median (the middle value) is less than the mean (the average) and the mode (the most frequent value) is less than both the median and the mean.

You have a rather strange die: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. You roll the die until you get a B. What is the probability that the first B appears on the first or the second roll?

A. .333
B. .704
C. .556
D. .037
E. .296

Answers

Answer:

C. .556

Step-by-step explanation:

Given that you have a rather strange die: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. You roll the die until you get a B.

Probability of getting A = [tex]\frac{3}{6}[/tex]

Probability of getting B = [tex]\frac{2}{6}[/tex]

Probability of getting c = [tex]\frac{1}{6}[/tex]

Each throw is independent of the other

the probability that the first B appears on the first or the second roll

= P(B) in I throw +P(B) in II throw

= P(B) in I throw + P(either A or C) in I throw*P(B) in II throw

=[tex]\frac{2}{6}+\frac{4}{6}*\frac{2}{6}\\=\frac{5}{9} \\=0.556[/tex]

Option c is right

subtract: (−2x2 + 9x − 3) − (7x2 − 4x + 2) −9x2 − 13x + 5 −9x2 + 13x − 5 5x2 − 13x − 1 5x2 + 5x − 5

Answers

Answer:

17x² - 5x + 11 = 0

Step-by-step explanation:

To add or subtract a polynomial do the operation with like - terms.

i.e., Two terms of x² gets added or subtracted. Similarly terms of x and constant.

Here, we have to subtract:

[tex]$ 2x^2 + 9x - 3 - 7x^2 + 4x - 8 - 9x^2 - 13x + 5 - 9x^2 + 13x - 5 + 5x^2 - 13x - 1 + 5x^2 + 5x - 5 $[/tex]

Club all the like terms for easier simplification. We get:

[tex]$ (-2 - 7 - 9 - 9 + 5 + 5)x^2 + (9 + 4 - 13 + 13 - 13 + 5)x + (-3 - 2 + 5 - 5 - 1) $[/tex]

[tex]$ \implies - 17 x^2 + 5x - 11 = 0 $[/tex]

Multiplying by -1 throughout:

17x² - 5x + 11 = 0 is the answer.

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A random sample of 16 residents of Wilmington, Delaware, had a mean of $52,500 with a standard deviation of $9,500. At the .05 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?



(a) State the null hypothesis and the alternate hypothesis.



H0: µ =

H1: µ >


--------------------------------------------------------------------------------



(b) State the decision rule for .05 significance level. (Round your answer to 3 decimal places.)


Reject H0 if t >


(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)


Value of the test statistic

Answers

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $44,500

Sample mean, [tex]\bar{x}[/tex] = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s =  $9,500

a) First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}[/tex]

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37[/tex]

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

[tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex]

Since,                    

[tex]t_{stat} > t_{critical}[/tex]

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income  than the national average

A manufacturer of coffee vending machines has designed a new, less expensive machine. The current machine is known to dispense (into cups) an average of 7 fl. oz., with a standard deviation of .2 fl. oz. When the new machine is tested using 15 cups, the mean and the standard deviation of the fills are found to be 7 fl. oz. and .219 fl. oz. Test H0: σ = .2 versus Ha: σ ≠ .2 at levels of significance .05 and .01. Assume normality. (Round your answer to 4 decimal places.)

Answers

Answer:

[tex] t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864[/tex]

[tex]p_v = 2*P(\chi^2_{14}>16.786)=0.5355[/tex]

And the 2 is because we are conducting a bilateral test.

[tex]\alpha=0.05[/tex] since the the [tex]p_v >0.05[/tex] we fail to reject the null hypothesis.

[tex]\alpha=0.01[/tex] since the the [tex]p_v >0.01[/tex] we fail to reject the null hypothesis.

Step-by-step explanation:

Data given

[tex]\mu=7[/tex] population mean (variable of interest)

[tex]\sigma=0.2[/tex] represent the population standard deviation

[tex]s=0.219[/tex] represent the sample deviation

n=15 represent the sample size

[tex]\alpha=0.05,0.01[/tex] represent the values for the significance level  

Hypothesis test

On this case we want to check if the population standard deviation is equal or not to 0.2, so the system of hypothesis are:

H0: [tex]\sigma = 0.2[/tex]

H1: [tex]\sigma \neq 0.2[/tex]

In order to check the hypothesis we need to calculate the statistic given by the following formula:

[tex] t=(n-1) [\frac{s}{\sigma_o}]^2 [/tex]

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

[tex] t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864[/tex]

P value

We know the degrees of freedom of the distribution 14 on this case and we can find the p value like this:

[tex]p_v = 2*P(\chi^2_{14}>16.786)=0.5355[/tex]

And the 2 is because we are conducting a bilateral test.

[tex]\alpha=0.05[/tex] since the the [tex]p_v >0.05[/tex] we fail to reject the null hypothesis.

[tex]\alpha=0.01[/tex] since the the [tex]p_v >0.01[/tex] we fail to reject the null hypothesis.

Final answer:

The question involves hypothesis testing for variance in relation to a coffee vending machine. After calculating the test statistic (using the Chi-square test) and comparing it with critical values at .05 and .01 significance levels, we fail to reject the null hypothesis. This means that there's not enough statistical evidence to suggest that the new machine has different variability in coffee amounts dispensed compared to the old machine.

Explanation:

To solve this problem, you need to use hypothesis testing for variance. Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. In hypothesis testing, an initial claim or belief about a population is translated into two competing hypotheses, the null hypothesis and the alternative hypothesis.

In this case, the null hypothesis(H0) is that the variance σ² is equal to 0.04 (σ=0.2; σ^2 = (0.2)² = 0.04), and the alternative hypothesis(Ha) is that the variance is not equal to .04.

The test statistic for this hypothesis is the Chi-Square statistic. It's calculated using the formula:

[ (n-1)*s² ] / σ²

where n is the sample size, σ² is the variance under the null hypothesis and s² is the empirical or sample variance. In your case, n = 15, σ² = 0.04 and s² = (0.219)² = 0.047961.

Substituting the values, we get (chi-square) χ² = (15-1)*(0.047961)/0.04 = 0.5995125.

The degrees of freedom (df) in this context is (n-1) = 14. At .05 level of significance, for 14 degrees of freedom, the critical values of χ² are 6.571 and 23.684. Likewise, for .01 level of significance, critical values are 3.787 and 30.578.

The calculated statistic (0.5995125) falls between these ranges for both cases, so we fail to reject the null hypothesis at both .05 and .01 significance level. Hence, the manufacturer does not have enough evidence to suggest that the new machine has a different variability in the amount of coffee dispensed compared to the old machine.

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jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit.f(t)=2430(1.04)^28a. rewrite the equation in the form f(t)=A(1+r/n)^ntb. what is the annual interest rate? So for those that are still at the same place, as I was so long ago psychologically abused as i was damaged. By a decade of abuse of impoverishment. I'm so much stronger after more then 900 days ago. If I could, well I pray you do as I will. Name the stages of alternation of generations. Specify whether the stage is diploid or haploid Pronation of the forearm involves the inward movement of the forearm in which of the following planes?Select one:a. Transverseb. Anterior-posteriorc. Sagittal Incorrectd. Frontal In the fourth paragraph the word enclosure means A)closet. B)container. C)pond. D)shell. PICTURE BELOW Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?A)2B)3C)4D)5 When the termination is a terminal block, care must be taken to ensure a good electrical connection without damaging the conductor. Terminals should not be used for more than ? conductor(s), unless they are identified for such usea) oneb) twoc) three A program contains a seven-element array that holds the names of the days of the week. At the start of the program, you display the day names using a subscript named dayNum. You display the same array values again at the end of the program, where you as a subscript to the array.a. must use dayNumb. can use dayNum, but can also use another variablec. must not use dayNumd. must use a numeric constant instead of a variable When Miguel feels that life is really getting to him, he has one very close friend with whom he can share anything. This friend, Anitra, never judges him and is supportive in any way that she can be. Anitra is serving as a ________ to Miguel. A 0.454-kg block is attached to a horizontal spring that is at its equilibrium length, and whose force constant is 21.0 N/m. The block rests on a frictionless surface. A 5.90102-kg wad of putty is thrown horizontally at the block, hitting it with a speed of 8.97 m/s and sticking. Assume each of the variables set1 and set2 references a set. Write code that creates another set containing all the elements of set1 and set2, and assigns the resulting set to the variable set3. Scott Peterson was convicted by a jury of murdering his wife and unborn son. Therefore, he must have actually committed these crimes.a) Inductive-soundb) inductive-strongc) deductive-invalidd) inductive-weake) deductive-valid Gonda, Herron, and Morse is considering possible liquidation because partner Morse is personally insolvent. The partners have the following capital balances: $60,000, $70,000, and $40,000, respectively, and share profits and losses 30%, 45%, and 25%, respectively. The partnership has $200,000 in noncash assets that can be sold for $150,000. The partnership has $10,000 cash on hand, and $40,000 in liabilities. What is the minimum that partner Morse's creditors would receive if they have filed a claim for $50,000? Please show the work.A. $0.B. $27,500.C. $45,000.D. $47,500.E. $50,000. Tchaikovsky is known primarily for his ballets. True False In a status report, executives want to know not only where we are today, but also where we will end up. Calculating where we will end up financially is not as easy as it sounds. Selecting the wrong formula can leave the executives and customers with a faulty impression. There are several formulas available for the calculation of the estimated cost at completion (EAC). For simplicity, consider the following three formulas:EAC = (ACWP/BCWP) x (budget at completion)EAC = ((ACWP/BCWP) x (BCWS for work completed and in progress)) + (planned or revised planned costs of work packages not yet begun)EAC = (actual to date) + (all remaining work, including work in progress,to be completed at the planned or budgeted costs)a. Using the table below, determine the value of EAC for each of the three formulas. Assume that A, B, and C are the only work packages in the project, and BCWS(Total) is the total value for PV for each work package rather than PV for the reporting period. Use the following formula for calculating EV:EV = (% Complete) x BCWS(Total)Activity % Complete BCWS(Total) ACWPA 100 1000 1100B 50 1000 800C 0 1000 0 Which of the following equations best describes a square root function that is reflected across the x-axis and has a vertex of (4,2)?A. [tex]y=\sqrt{-(x-4)} +2[/tex]B. [tex]y= -\sqrt{x+2}-4[/tex]C. [tex]y=-\sqrt{x+4} +2[/tex]D. [tex]y=-\sqrt{x-4} +2[/tex] The diagram below depicts the international flow of funds in the 1920s. What does the number 1 represent in the diagram? Abigail Jones is a sales executive at Orbit Bank in Brussels. She is the best performer on her team and often gets the highest number of corporate accounts for the company. However, she feels that she does not get sufficient credit for her hard work. During lunch, she says to her colleague, "I have been getting the largest accounts for the bank for the past eight months. Yet, my manager never acknowledges the kind of effort I put in to get these accounts." Which component of attitude is being demonstrated by Jones? Why would anyone want to downplay the role of the translator? Provide a detailed explanation of the water cycle and how plants are involved with this process. Steam Workshop Downloader