Answer:
(About) 20043.46 after 14 years
Step-by-step explanation:
~ Let us apply a compound interest formula not through substituting values, but through a similar way of following this formula ~
1. First let us assign the values:
interest ⇒ 6.5 percent ( % ), principle number - start value ⇒ $ 8300, time ⇒ 14 years
2. Now let us convert interest ⇒ decimal form: 0.065
3. Add 1 to this value 0.065 ⇒ 1 + 0.065 = 1.065
4. Now let us take 1.065 exponentially to the power of itself 14 times, or in other words to the power of time ( 14 years ): 1.065^ 14 = 2.414874185.......
5. Multiply this infinite number by the principle number P, or most commonly known as the start value: 2.414874185....... * 8300 ⇒
(About) 20043.46 after 14 years
Using the formula for compound interest and substituting accordingly, the given investment grows to approximately 18,108.80 dollars after 14 years.
Explanation:To solve this, we'll use the formula for compound interest, which is P(1 + r/n)^(nt), where P is the principle amount (initial investment), r is the annual interest rate, n is the number of times that interest is compounded per unit t, and t is the time the money is invested for.
In this case, P = 8300 dollars, r = 6.5/100 = 0.065 (we need the rate in decimal form), n = 1 (since the interest is given annually), and t = 14 years.
Substitute these values into the formula:
A = 8300(1 + 0.065/1)^(1*14) which simplifies to A = 8300(1.065)^14.
Using a calculator, A ≈ 18,108.80 dollars. So, after 14 years, the account will have approximately 18,108.80 dollars.
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When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 32% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 45 of the dragon eggs to incubate. Consider all the possible samples of 45 dragon eggs. What is the usual number of yellow eggs in samples of 45 eggs
Answer:
The usual number of yellow eggs in samples of 45 eggs is 14.4.
Step-by-step explanation:
For each egg, there are only two possible outcomes. Either they are yellow, or they are not. The probability of an egg being yellow is independent of other eggs, so we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
32% of the eggs are yellow
This means that [tex]p = 0.32[/tex]
45 eggs
This means that [tex]n = 45[/tex]
What is the usual number of yellow eggs in samples of 45 eggs
[tex]E(X) = np = 45*0.32 = 14.4[/tex]
The usual number of yellow eggs in samples of 45 eggs is 14.4.
In a random sample of 45 dragon eggs on planet Pern, we would typically expect around 14 to 15 eggs to be yellow, based on the given probability of an egg being yellow (which is 32%).
Explanation:The subject of the question relates to probabilities in statistics. Here, we are given that the chance a dragon's egg on planet Pern is yellow is 32% or 0.32 in decimal form. We are then asked to predict the number of yellow eggs in a group of 45 eggs.
To solve this, we simply multiply the total number of eggs by the notation of the probability:
45 eggs * 0.32 = 14.4
However, you can't have 0.4 of an egg, so we have to round this number to 14 or 15 eggs. Therefore, in a random sample of 45 dragon eggs, we would typically expect around 14 to 15 of them to be yellow assuming that the probability remains constant.
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To find the surface area of the figure shown, Mia found the surface area of the two triangular prisms and the rectangular prism. From this, Mia subtracted 6 ft2. Did Mia make an error?
Mia should have subtracted 16 square feet.
Mia needs to subtract another 6 square feet.
Mia must calculate each triangle separately.
There is no error—Mia is correct.
Answer:
Mia needs to subtract another 6 square feet
Step-by-step explanation:
Guessed it and got it right
Answer:
needs to subtract another 6 ft
Step-by-step explanation:
How many solutions does the equation 3(x + 2) – 10 = 4x – 6 + x have?
Answer:
1
Step-by-step explanation:
3(x+2)-10=4x-6+x
3x+6-10=5x-6
2x=2
x=1
This is the only solution to this equation, meaning that there is only one solution to the equation. Hope this helps!
The equation 3(x + 2) - 10 = 4x - 6 + x has one solution, which is x = 1. After simplifying the equation and solving for x, we confirm that substituting x = 1 back into the equation results in an identity, indicating that this is the correct solution.
To determine how many solutions the equation 3(x + 2) \\- 10 = 4x \\- 6 + x has, we must first simplify the equation and solve for x.
Let's simplify both sides of the equation:
Distribute the 3 on the left side: 3x + 6 \\- 10 = 4x \\- 6 + x.
Combine like terms on the right side: 3x \\- 4 = 5x \\- 6.
Get all the x terms on one side and constants on the other: 3x \\- 5x = \\-6 + 4.
Simplify the equation: \ -2x = \\-2.
Divide both sides by \\-2 to solve for x: x = 1.
So, the solution to the equation is x = 1. To verify that this is the solution, we can substitute x = 1 back into the original equation and check that it holds true, which would confirm that the equation is an identity. In this case, the substitution leads to an identity, confirming that x = 1 is the correct and only solution to the equation.
Jane wants to buy a movie that costs $15.49. She has $8.75. How much more money does Jane need to buy the movie?
Answer:
$6.74
Step-by-step explanation:
Subtract 15.49 and 8.75
Answer: 6.74.
Step-by-step explanation: I took the quiz before!
Hope this helps! (✪ ω ✪)
statistical analyst for the Wall Street Journal randomly selected six companies and recorded both the price per share of stock on January 1, 2009 and on April 30, 2009. The results are presented below. Suppose the analyst wished to see if the average price per share of stock on April 30, 2009 is greater than the average price per share of stock on January 1, 2009 at α=.025. Apr. 30, 2009 33 33 34 30 33 38 Jan. 1, 2009 21 25 30 33 23 27 For the hypothesis stated above, what is the P-value?
Answer:
p value= 2.228
Step-by-step explanation:
since average of two groups is being compared two-sample t-test will be performed.
degrees of freedom= 12-2=10
at α=.025 from t table
p value= 2.228
Find an equation of the circle that has center(-3,4) and passes through(1,-2)
Answer:
(x +3)^2 +(y -4)^2 = 52
Step-by-step explanation:
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
We are given the value of (h, k), and we can find the value of r^2. Using the values of h and k, our equation is ...
(x +3)^2 +(y -4)^2 = r^2
Since we know this equation is satisfied by the point (1, -2), we can use this point in the equation to find r^2:
(1 +3)^2 +(-2 -4)^2 = r^2
16 +36 = r^2 = 52
The equation of the circle is ...
(x +3)^2 +(y -4)^2 = 52
3. Erin's soccer team has won 17 of
their 20 games this season. What is
the probability that they will win their
next game?
Answer:
They have a 85% chance of winning their next game.
Step-by-step explanation:
100÷20 = 5
17×5=85
So, they have a 85% chance of winning their next game.
Hope This helped!!!!! :)
A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the store's in-house credit card versus using a Visa, Mastercard, or one of the other major credit cards. To do this, it has randomly selected a sample of customers who have made one or more purchases with each of the types of credit cards. The following represents the results of the sampling. In-House Credit Card National Credit Card Sample Size: 86 113 Mean Monthly Purchases: $45.67 $39.87 Standard Deviation: $10.90 $12.47 Suppose that the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level of 0.05, what is the value of the test statistic assuming the standard deviations are known? Round to two decimal places.
A gardener is planting two types of trees: Type A is 8 feet tall and grows at a rate of 7 inches per year. Type B is 2 feet tall and grows at a rate of 13 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
1 year
Step-by-step explanation:
8 + 7x = 2 + 13x
Move the 2 to the other side by subtracting 2 from both sides.
6 + 7x = 13x
Move the 7x to the other side by subtracting both sides by 7x.
6 = 6x
Divide both sides by 6.
1 = x
Therefore, x equals 1 and it will take 1 year for both trees to reach the same height.
5. Melanie scored 20/25 on her quiz. What percent is this equal to? *
Answer:
0.8 or 80%
Step-by-step explanation:
To easily find percents, divide the numerator with the denominator. Or, first you can simplify the fraction first.
20/25 can be divided by 5. Which is 4/5.
4/5=0.8
So, the answer is 80%
Answer:
80%
Step-by-step explanation:
[tex]\frac{20}{25} = \frac{4}{5}[/tex]
To find the percentage, multiply by 100:
[tex]\frac{4}{5} * 100 = 80[/tex]
Bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a diving lesson on May 5, when will be the next date on which she has both swimming and diving lessons?
Answer:
The 20th of May
Step-by-step explanation:
I made a chart like a calendar and started on the 5th of may and counted every 5 days for the swimming lessons and every 3 days. Then I saw when she had both swimming and driving lessons and the first time after the 5th is the 20th.
Answer:
Bridget will have both swimming and diving lessons on the 15th.
A sociologist develops a test to measure attitudes towards public transportation, and 25 randomly selected subjects are given the test. The sample mean score is 76.2 and the sample standard deviation is 21.4. The population is normally distributed. What is the 95% confidence interval for the mean score of all such subjects? Round to 3 decimal places.
Final answer:
The 95% confidence interval for the true mean score of subjects' attitudes towards public transportation is between 67.361 and 85.039, computed using a t-score for a sample size of 25.
Explanation:
To calculate the 95% confidence interval for the mean score of all subjects regarding their attitudes towards public transportation, we will use the following formula for a confidence interval when the population is normally distributed but the population standard deviation is not known:
CI = ± t*(s/√n), where CI is the confidence interval, ± denotes plus or minus, t is the t-score that corresponds to the desired level of confidence and degrees of freedom (df = n - 1), s is the sample standard deviation, and √n is the square root of the sample size.
For our sample size of n = 25, the degrees of freedom is df = 24. Consulting a t-distribution table or using statistical software to find the t-value for df = 24 at a 95% confidence level, we assume a t-value approximately equal to 2.064 (this may slightly vary depending on the source of the t-distribution table). Plugging in the values:
CI = ± 2.064*(21.4/√25), thus the margin of error is approximately 2.064 * 4.28
The confidence interval is then the sample mean ± the margin of error:
76.2 ± (2.064 * 4.28)
This calculation yields a confidence interval for the population mean score of:
Lower Bound = 76.2 - 8.83872 ≈ 67.361
Upper Bound = 76.2 + 8.83872 ≈ 85.039
Therefore, rounding to three decimal places: 67.361 (Lower Bound) and 85.039 (Upper Bound).
We are 95% confident that the true mean score of all subjects' attitudes towards public transportation lies between 67.361 and 85.039.
A dietitian wants to know the average time spent on breakfast in a primary school. The dietitian randomly samples 16 students and finds that the average is 15.8 minutes with a standard deviation of 2.31 minutes. Assume that the distribution of the time spent on the breakfast is normally distributed. The dietitian finds a 90% confidence interval for this sample is (14.788, 16.812) Flag question Select one or more:_________. a. The margin of error is 1.012. b. The margin of error is 2.024 c. The margin of error is 0.950 d. We believe that the true mean time spent on breakfast in this primary school is between 14.788 and 16.812 minutes. e. If we take many other samples from this population, 90% of them will have a sample mean that is between 14.788 and 16.812. f. There is a 90% chance that the true mean is between 14.788 and 16.812 minutes.
Answer: is their any picture? or an example?
The equation y= 2x represents a set of data.
Which statement is NOT true?
Answer:
2 is an initial value
tell me if its right because i garuntee it is
4. The null hypothesis for the chi-square goodness-of-fit test states that the distribution of A. cases for each group is equal to the expected distribution based on theory/knowledge of the population. B. sample means is equal to expectation based on the expected frequency. C. sample means for each group is equal. D. the sample means is equal to the expected distribution based on theory/knowledge of the population.
Answer:
D. the sample means is equal to the expected distribution based on theory/knowledge of the population.
Step-by-step explanation:
The Chi square goodness-of-fit test is used in statistical analysis to determine if the observed value in a collection of data, is significantly different from the expected value. Theoretical distribution which could be classified as normal, binomial, or poisson, are compared against the empirical distribution.To run a chi square goodness-of-fit test, we first formulate the null and alternate hypothesis. The degrees of freedom are then observed from the data given and the hypothesis is tested.
The null hypothesis assumes that the observed frequencies are equal to the expected frequencies. If there is a considerable difference, then the null hypothesis is rejected.
1. Write an expression that represents the area of a rectangle given that the Length = (x+3) and the width = (3x + 4).
2. The area of a rectangle is 28x2 – 13xy – 6y2 square units. If the length of the rectangle is 7x + 2y units, then find the breadth of the rectangle, hence find the perimeter of the rectangle
Answer:
(7x+2y)- length (4x-3y)- width
22x-2y is the perimeter.
Step-by-step explanation:
A researcher wanted to test his claim that the mean walking pace of business
travelers is different from that of leisure travelers at the airport. To test his claim he
obtained the following lists of 9 business and 8 leisure travelers. Test his claim at the
.05 = level of significance.
Business
Travelers
42 31 37 45 49 52 43 39 45
Leisure
Travelers
32 29 35 40 38 34 42 33
Answer:
[tex] t = \frac{42.56-35.375}{\sqrt{\frac{6.327^2}{9} +\frac{4.34^2}{8}}}=2.755[/tex]
The degrees of freedom are given by:
[tex] df=n_1 +n_2-2 =9+8-2= 15[/tex]
Since we have a two tailed test the p value can be calculated like this:
[tex] p_v=2* P(t_{15} >2.755) = 0.0147[/tex]
And since the p value is lower than the significance lvel given of 0.05 we have enough evidence to conclude that we have significant differences between the two groups on this case.
Step-by-step explanation:
We have the following data given:
Business Travelers
42 31 37 45 49 52 43 39 45
Leisure Travelers
32 29 35 40 38 34 42 33
For this case we need to begin finding the sample mean and deviations for each group with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And we got:
[tex] \bar X_1 = 42.56[/tex] represent the sample mean for the Business travelers
[tex]s_1 = 6.327[/tex] represent the sample deviation for the Business travelers
[tex]n_1= 9[/tex] the sample size for the Business travelers
[tex] \bar X_2 = 35.375[/tex] represent the sample mean for the Leisure travelers
[tex]s_2 =4.34[/tex] represent the sample deviation for the Leisure travelers
[tex]n_2= 8[/tex] the sample size for the Leisure travelers
The system of hypothesis for this case are:
Null hypothesis: [tex] \mu_1 =\mu_2[/tex]
Alternative hypothesis: [tex] \mu_1 \neq \mu_2[/tex]
The statistic for this case is given by:
[tex] t =\frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}[/tex]
And replacing we got:
[tex] t = \frac{42.56-35.375}{\sqrt{\frac{6.327^2}{9} +\frac{4.34^2}{8}}}=2.755[/tex]
The degrees of freedom are given by:
[tex] df=n_1 +n_2-2 =9+8-2= 15[/tex]
Since we have a two tailed test the p value can be calculated like this:
[tex] p_v= 2*P(t_{15} >2.755) = 0.0147[/tex]
And since the p value is lower than the significance lvel given of 0.05 we have enough evidence to conclude that we have significant differences between the two groups on this case.
The minute hand on a clock is 9 centimeterslong and travels through an arc of 252° every 42 minutes. To the nearest tenth of a centimeter, how far does the minute handtravel during a 42-minute period?
Answer: the minute hand travel 39.6 cm
Step-by-step explanation:
Length of minute hand of a clock = 9 cm
Central angle made by the minute hand = 252°
To find: how far the minute hand travel
Therefore
Length of minute hand is equal to the radius of circle
As we know the circumference of a circle is given by
[tex]C= 2\pi r \dfrac{\theta}{360^\circ}[/tex] where C is circumference , r is radius and ∅ is the central angle
So we have
[tex]C= 2 \times \dfrac{22}{7} \times 9 \times \dfrac{252^\circ}{360^\circ} \\\\\Rightarrow C= 2 \times \dfrac{22}{7} \times \dfrac{252^\circ}{40^\circ} \\\\\Rightarrow C= \dfrac{11}{7} \times \dfrac{252^\circ}{10^\circ} = 39.6[/tex]
Hence, the minute hand travel 39.6 cm in 42 minute period
Final answer:
The minute hand of the clock, which measures 9 centimeters in radius, travels approximately 39.3 centimeters along the arc when it moves through a 252-degree central angle in a 42-minute period.
Explanation:
To determine how far the minute hand of a clock travels in a 42-minute period, we need to calculate the arc length, which is a portion of the circumference of the circle traced by the minute hand's tip. We are given that the minute hand is 9 centimeters long, meaning it is the radius of the circle, and it travels through an arc of 252° during a period of 42 minutes.
The formula to calculate the arc length is:
ℓ = θ/360 × 2πr
Where:
ℓ is the arc length
θ is the central angle in degrees
r is the radius of the circle
In this case:
θ = 252°
r = 9 cm
Now, let's substitute these values into the formula:
ℓ = 252/360 × 2 × π × 9
ℓ ≈ 0.7 × 2 × 3.14159 × 9
ℓ ≈ 39.27 cm
So, to the nearest tenth of a centimeter, the minute hand travels approximately 39.3 cm during a 42-minute period.
The speed of pickup of ride sharing services like Uber and Lyft seems to have surpassed that of ambulance services. The mean response time of ambulances across the United States is 15.3 minutes with a standard deviation of 12.8 minutes. For ride sharing services, the mean pick-up time across the United States is 8 minutes with a standard deviation of 5.2 minutes. Based on these estimates, which of the following gives the standard deviation of the sampling distribution of the difference in the sample means for samples of 30 ambulance rides and 40 ride sharing rides (Ambulance – Ride Sharing)?
Answer:
The correct answer is (C).
Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately≈2.912 minutes.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct answer is (C).
Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} = \sqrt{\frac{12.8^2}{30}+\frac{5.2^2}{40}} \approx 2.912
n
1
s
1
2
+
n
2
s
2
2
=
30
12.8
2
+
40
5.2
2
≈2.912 minutes.
Which of the following is the equation of a direct variation that has a constant of variation equal to -1/2?
A. y= x- 1/2
B. -1/2 y=x
C. y= -2x
D. y= -1/2x
I think it is c. y= -2x hope you have a good day!
Lauren plans to deposit $6000 into a bank account at the beginning of next month and $225/month into the same account at the end of that month and at the end of each subsequent month for the next 4 years. If her bank pays interest at a rate of 3%/year compounded monthly, how much will Lauren have in her account at the end of 4 years?
Answer:
$18206.5
Step-by-step explanation:
Considering, r = interest rate
n = number of intervals
t = duration of the payment
A = monthly installment
PV = Present Value
FV = Final Value
Using the formula
FV=PV (1+ r/n[tex])^{nt-1[/tex] + a((1+ r/n[tex])^{nt[/tex]-1/[tex]\frac{r}{n}[/tex])
FV=6000[tex](1+ \frac{0.03}{12} )^{(12)(4)-1} +225\frac{(1+0.03/12)^{(12)(4)}-1 )}{0.03/12}[/tex]
FV= 6747 + 11459.5
FV=18206.5
Her balance in 4 years is $18206.5
3x^2 + 18x + 27 = 0 can you solve for x
Answer:
3x^2 + 18x + 27 = 0
<=> 3(x^2 + 6x + 9) = 0
<=> 3(x + 3)^2 = 0
<=> x = -3
Hope this helps!
:)
Sherry is cooking chicken for her family. She wants to be sure the chicken has an internal temperature of at least 170 degrees Fahrenheit. She uses a thermometer to measure the internal temperature at four randomly chosen places. The minimum reading in the sample is 180 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic. Population, minimum temperature of 170 degrees Fahrenheit; parameter, all chicken meat temperature readings; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit Population, all chicken meat temperature readings parameter, minimum temperature of 170 degrees Fahrenheit; sample, minimum sample reading of 180 degrees Fahrenheit; statistic, four random thermometer readings Population, four random thermometer readings; parameter, all chicken meat temperature readings; sample, minimum temperature of 170 degrees Fahrenheit; statistic, minimum sample reading of 180 degrees Fahrenheit Population, all chicken meat temperature readings; parameter, minimum temperature of 170 degrees Fahrenheit; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit Population, minimum sample reading of 180 degrees Fahrenheit; parameter, all chicken meat; sample, minimum temperature of 170 degrees Fahrenheit; statistic, four random thermometer readings
Answer:
Population, all chicken meat; parameter, minimum temperature of 170 degrees Fahrenheit; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit
Step-by-step explanation:
Help whats 2+2 please i cant figure it out its baby two right
2 + 2 =4 is four tgvjixyi9
Answer:
It’s 4 or fish
Step-by-step explanation:
A brokerage charges ? regardless of whether an investor buys or sells assets, and ? are incurred with every transaction
Answer:
Yes, that's true.
Step-by-step explanation:
A brokerage fee is the commission paid to a salesperson or broker for selling insurance or securities, respectively. The amount of this fee is usually calculated as a percentage of the transaction price, though it may be a flat fee.
brokerage fee compensates a broker for executing a transaction. It is usually, but not always, a percentage of the transaction value. In finance, stockbrokers most often come to mind, but real estate agents and business brokers frequently charge brokerage fees
Answer:
A brokerage charges brokerage account fees regardless of whether an investor buys or sells assets, and trade commissions are incurred with every transaction.
73 POINTS need help
A large mall is built in the shape of a square. At each corner of the mall stands a pillar which is topped by a pyramid-shaped section of red tin roof, as shown in the picture below.
The pyramid is a square pyramid, measuring 21.5 feet on each of its base edges. The height of each of the triangular lateral face is 13.4 feet. Use this information to answer the following questions.
What is the area of the roof? [Type your answer as a number. Do not round.]
blank square yards
Answer:
2304.8 ft^2
Step-by-step explanation:
The lateral area of one of the pyramid is 21.5 * 13.4 * 4/2 = 576.2
There are 4 of them, so we multiply that by 4 : 576.2 * 4 = 2304.8
P
Q
R
S
T
-10
-8
6
4
2
0
2
4
6
Find the midpoint of PS.
On Monday, 288 students went on a trip to the zoo. All 7 buses were filled and 8 students had to travel in cars. How many students were in each bus?
Answer:
40 kids
Step-by-step explanation:
288 minus the 8 kids that had to hide in cars= 280. 280 divided by the seven busses is 40
Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that less than thirty percent of the teen girls smoke to stay thin? g
Answer:
We conclude that less than thirty percent of the teen girls smoke to stay thin.
Step-by-step explanation:
We are given that the Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old).
After four years the girls were surveyed again. Sixty-three said they smoked to stay thin.
Let p = percentage of the teen girls who smoke to stay thin.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 30% {means that at least thirty percent of the teen girls smoke to stay thin}
Alternate Hypothesis, [tex]H_A[/tex] : p < 30% {means that less than thirty percent of the teen girls smoke to stay thin}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample % of teen girls who smoke to stay thin = [tex]\frac{63}{273}[/tex] = 0.231
n = sample of teen girls = 273
So, test statistics = [tex]\frac{0.231-0.30}{\sqrt{\frac{0.231(1-0.231)}{273} } }[/tex]
= -2.705
The value of z test statistics is -2.705.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical value of -1.645 for left-tailed test.
Since our test statistics is less than the critical value of z as -2.705 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that less than thirty percent of the teen girls smoke to stay thin.
About 23% of the surveyed girls smoked to maintain or lose weight. Social and cultural factors contribute to this behavior, which often leads to health issues. Broader and more comprehensive studies are needed for a conclusive answer.
Explanation:Yes, there's some evidence to suggest fewer than thirty percent of teen girls smoked to stay thin. Only 63 girls out of the 273 surveyed stated they smoked for weight issues, which equates to around 23%. However, this result is not conclusive, as it is based solely on the girls who participated in this particular study. For a more comprehensive conclusion, we would need to evaluate multiple studies with larger participant samples.
In broader context, the challenges teens face with self-image are due in part to sociocultural factors, such as the beauty ideal of thinness often emphasized in media. The image of thin models contributes significantly to body image concerns and associated behaviours like smoking to maintain or lose weight. Such behaviours can lead to health problems including, but not limited to, type 2 diabetes, heart disease, and even cancer.
Also, obesity is a rising epidemic affecting many, with its highest rates found in the United States. Increasing awareness about these issues and promoting healthier methods of maintaining weight can help in addressing these problems.
Learn more about Teen smoking for thinness here:https://brainly.com/question/12743744
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According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing LaTeX: H_0H 0: LaTeX: p=0.173p = 0.173 versus LaTeX: H_aH a: LaTeX: p<0.173p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth-graders surveyed had used marijuana. Are conditions met for use of the normal model to represent the distribution of sample proportions?
Answer:
The conditions for use of the normal model to represent the distribution of sample proportion are not met. He should increase the sample size until the conditions are met.
If the test is done anyway, the null hypothesis failed to be rejected.
The conclusion is taht there is not enough evidence to support the claim that the percentage is lower in this district.
Step-by-step explanation:
The conditions for use of the normal model to represent the distribution of sample proportion are not met, as the affirmative responses are less than 10.
[tex]np=80*0.1=8<10[/tex]
If the test of hypothesis is done as if the conditiones were met, we know that the claim is that the percentage is lower in this district.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.173\\\\H_a:\pi<0.173[/tex]
The significance level is 0.05.
The sample has a size n=80.
The sample proportion is p=0.1.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.173*0.827}{80}}\\\\\\ \sigma_p=\sqrt{0.001788}=0.042[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.1-0.173+0.5/80}{0.042}=\dfrac{-0.067}{0.042}=-1.578[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-1.578)=0.057[/tex]
As the P-value (0.057) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the percentage is lower in this district.