Answer:
The cash paid to the bondholder on July 1 is Z = $7000
Step-by-step explanation:
From the question we are told that
The percentage bond issued by the company is [tex]n = 7[/tex]%
The par value of the bond is [tex]V =[/tex]$200,000
The market rate is [tex]r = 6[/tex]%
So we are told that the bonds pay interest semiannually on January 1 and July
So the cash paid to the bondholder on July 1 is mathematically evaluated as
Z = [tex]V * \frac{7}{100} * \frac{1}{2}[/tex]
substituting value
Z = [tex]200000 * \frac{7}{100} * \frac{1}{2}[/tex]
Z = $7000
Final answer:
The cash paid on July 1 to bondholders for the company's 7% bonds with a par value of $200,000 is $7,000. This is calculated by first determining the annual interest payment and then dividing by two for the semiannual payment.
Explanation:
Understanding Bond Interest Payments
The question revolves around how much cash is paid to bondholders on July 1 for a company that issued 7% bonds with a par value of $200,000 at par when the market rate was 6%. Since the bonds were issued at par, this implies that the bond's stated interest rate matches the market interest rate at the time of issuance. However, the market rate later does not affect the fixed payments of a bond issued at par.
The interest payment for this bond would be calculated using the face value and the stated annual interest rate, which is then divided by two since interest is paid semiannually. The calculation is as follows:
Calculate the annual interest payment: $200,000 (par value) × 7% (interest rate) = $14,000.Divide the annual interest by two for the semiannual payment: $14,000 ÷ 2 = $7,000.Therefore, the cash paid on July 1 to the bond holder(s) is $7,000.
We need to compare volatility of multiple assets. As the assets have different variation ranges, e.g. a big stock versus a penny stock, it is useful to look at the coefficient of variation, not the standard deviation, as a measure of volatility. We have the following population data: Mean ($) 0.48 175.93 286.47 Standard deviation ($) 0.09 34.72 63.08 (a)[2] Give an equation for the coefficient of variation in percentage terms. (b)[6] Find volatility of the three assets. Use two decimals for percentages, e.g. 23.76%. (c)[2] Which asset is the least volatile? Which asset is the most volatile?
Answer:
Check the explanation
Step-by-step explanation:
a)
the formula is given by,
c.v.=[tex]\frac{\sigma}{\mu}\times 100[/tex]
where is standard deviation and is mean of the given data.
b)for asse A,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 0.03 5 , 100 0,30 x 0.30 = 10%
for asse B,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 1.50 x 100 26005 × 100 =8.27 %
for asset C,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 18.70 × 100 =10.71%
c)since, c.v. of asset B is least, it is least volatile and c.v. of asset is most, it is most volatile.
Add the following numbers together: 80, 85, 90, 65, 80, 60
Answer:
Adding all the numbers together results in 460
Answer:
460 is the answer
Step-by-step explanation:
A bookstore marks up the price of a book by 25% of the cost from the publisher. Therefore, the
bookstore's price to the student, P(x) (in $) after a 5.3% sales tax, is given by P(x) = 1.053(x+0.25x),
where x is the cost from the publisher. Evaluate P(60) and interpret the meaning in context of this
problem. (Round to the nearest cent.)
P(60) = 78.98
When the bookstore spends $60 on a textbook, the student pays $78.98
P(60) = 78.98
When the bookstore pays $78.98 on a textbook, the student pays $60
P(60) = 47.39
When the bookstore pays $47.39 on a textbook, the student pays $60
P(60) = $47.39
The sales tax on a $60 textbook is $47.39
P(60) = 78.98
The sales tax on a $60 textbook is $78.98
P(60) = 47.39
When the bookstore pays $60 on a textbook, the student pays $47.39
Answer:
(A)
P(60) = 78.98 When the bookstore spends $60 on a textbook, the student pays $78.98Step-by-step explanation:
Given:
P(x) = 1.053(x+0.25x)
P(60) = 1.053(60+0.25*60)
=1.053(60+15)
=1.053(75)
P(60)=$78.98
Since x is the cost from the publisher, when the bookstore spends $60 on a textbook, the student pays $78.98.
The correct option is A.
The price of the book to the student is $78.98 when the bookstore spends $60 on the textbook.
Explanation:The subject of this question is Mathematics and it is suitable for High School students.
The problem involves calculating the price of a book after a markup and sales tax.
To evaluate P(60), we substitute x = 60 into the given expression P(x) = 1.053(x+0.25x).
P(60) = 1.053(60 + 0.25*60) = 1.053(60 + 15) = 1.053(75) = 78.975.
The bookstore's price to the student would be $78.98 when the bookstore spends $60 on a textbook.
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A certain ambulance service wants its average time to transport a patient to the hospital to be 10 minutes. A random sample of 12 transports yielded a 95 percent confidence interval of 11.8±1.6 minutes. Is the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital plausible based on the interval?
The claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital is false.
Given to us,average time to transport a patient = 10 minutes,sample of 12 transports yielded at 95% confidence interval is 11.8±1.6 minutes.SolutionWe know that, the confidence interval for any event shows as the interval with lower and upper bounds. Meaning it gives as the mean interval with a maximum and minimum possible values for that interval as well for unknown variables.
[tex]CI = \bar{x} \pm z \dfrac{s}{\sqrt{n}}[/tex]
where,
CI = confidence interval
[tex]\bar{x}[/tex] = sample mean
z = confidence level value
s = sample standard deviation
n = sample size
Similarly, given in sample of 12 transports yielded at 95% confidence interval is 11.8±1.6 minutes.
So, the mean interval is 11.8 minutes, with a lower bound as 10.2 minutes(11.8-1.6) while upper bound as 13.4 minutes(11.8+1.6).
Hence, the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital is false.
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Final answer:
The ambulance service's claim that their average transport time is 10 minutes is plausible since 10 minutes is within the provided 95% confidence interval of 11.8±1.6 minutes.
Explanation:
The question asks if the ambulance service's claim that their average time to transport a patient to the hospital is 10 minutes is plausible based on the provided 95% confidence interval. The confidence interval is given as 11.8±1.6 minutes, which means the interval ranges from 10.2 minutes to 13.4 minutes. Since 10 minutes is within this range, it is plausible that the true average transport time could be 10 minutes, although the intervals suggest that it is on the lower end of the sample's confidence interval.
Convert 65L into quarts
Answer:
68.68
Step-by-step explanation:
for an approximate result, multiply the volume value by 1.057
Let X and Y again be uniformly distributed independent random variables on [0, 1]. a) Compute the expected value E(XY ). b) What is the probability density function fZ(z) of Z = XY ? Hint: First compute the cumulative distribution function FZ(z) = P(Z ≤ z) using a double integral, and then differentiate in z. c) Use your answer to b) to compute E(Z). Compare it with your answer to a)
Answer:
a) Computing the expected value E(XY) gives 1/4
b) The probability density function fZ(z) of Z = XY is calculated in the attached picture.
c) Computing E(Z) gives 1/4
Step-by-step explanation:
Comparing the computation of E(Z) using the answer to b), it shows that the values are equal.
Cassie is climbing the stairs at a hotel. The base of the stairs is located at an altitude of 33 feet, and she ascends the stairs at a rate of 15 inches per
second. Josiah is descending from the top floor of the hotel in an elevator. He descends from 210 feet at a rate of 17.6 feet per second. Cassie begins
climbing the stairs at the same time Josiah begins descending in the elevator.
Which system of equations represents the number of seconds, x, it will take for Cassie and Josiah to be at the same altitude, y, in feet
The two equations expressing altitude y as a function of time in seconds x for Cassie and Josiah respectively are: y = 33 + 1.25x and y = 210 - 17.6x.
Explanation:The subject of this problem is linear equations in algebra. We set up two equations to represent the altitude changes of Cassie and Josiah over time.
Firstly, Cassie is ascending from a base level of 33 feet at a rate of 15 inches per second. However, the rate needs to be converted to feet per second because the initial altitude and the altitude Josiah is descending from are both in feet. So, 15 inches equals 1.25 feet (since 1 foot = 12 inches). Therefore, the altitude y Cassie reaches after x seconds can be represented as y = 33 + 1.25x.
Secondly, Josiah is descending from an altitude of 210 feet at a rate of 17.6 feet per second. Thus, the altitude y reached over x seconds can be given by y = 210 - 17.6x.
The system of equations therefore is:
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round 974657 to the nearest ten thousand
Answer:
970000
Step-by-step explanation:
a=40 c=41 what does b equal
considering this is a pythagorean theorem question (a^2+b^2=c^2)
then we can plug this in.
40^2+b^2=41^2
1600+b^2=1681 (subtract 1600 from both sides to isolate b)
b^2=81 (square root)
b=9
what is the meaning of range in the subject mathematics
range
Answer:
explanation
Step-by-step explanation:
The Range (Statistics) The Range is the difference between the lowest and highest values. Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. So the range is 9 − 3 = 6.
Answer:
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
An article predicts that "spit," spam that is delivered via internet phone lines and cell phones, will be a growing problem as more people turn to web-based phone services. In a poll of 5500 cell phone users, 19% indicated that they had received commercial messages and ads on their cell phones. Is there sufficient evidence that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year? (Use α = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.)z =
P =There is evidence to suggest that the proportion cell phone users who have received commercial messages or ads in 2004 is greater than the proportion of 0.13 reported for the previous year.
Answer:
We conclude that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year.
Step-by-step explanation:
We are given that in a poll of 5500 cell phone users, 19% indicated that they had received commercial messages and ads on their cell phones.
We have to test the claim that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year.
Let p = proportion of cell phone users who have received commercial messages or ads in 2004.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 0.13 {means that the proportion of cell phone users who have received commercial messages or ads in 2004 was smaller than or equal to the proportion of 0.13 reported for the previous year}
Alternate Hypothesis, [tex]H_A[/tex] : p > 0.13 {means that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year}
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 proportion of cell phone users who have received commercial messages or ads in 2004 = 19%
n = sample of cell phone users = 5500
So, test statistics = [tex]\frac{0.19-0.13}{\sqrt{\frac{0.19(1-01.9)}{5500}} }[/tex]
= 11.34
The value of z test statistics is 11.34.
Also, P-value of the test statistics is given by;
P-value = P(Z > 11.34) = 1 - P(Z [tex]\leq[/tex] 11.34)
= 1 - 0.9999 = 0.0001
Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.
Since our test statistics is way more than the critical value of z as 11.34 > 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 the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year.
Three students, Angie, Bradley, and Carnell, are being selected for three student council offices: president, vice president, and treasurer. In each arrangement below, the first initial of each person’s name represents that person’s position, with president listed first, vice president second, and treasurer third. Which shows the possible outcomes for the event?
ABC,
ABC, BAC, CBA
AAA, BBB, CCC
ABC, ACB, BCA, BAC, CAB, CBA
Answer:
The answer is D.Step-by-step explanation:
I got it right on the test.
Using the arrangements formula, it is found that the 6 possible outcomes for the event are given as follows:
ABC, ACB, BCA, BAC, CAB, CBA.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, there are three students, hence the number of outcomes in given by:
[tex]A_3 = 3! = 6[/tex]
And the outcomes are as follows:
ABC, ACB, BCA, BAC, CAB, CBA.
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what is the length of bc in the right triangle below
Answer:
20
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
12^2+16^2 = c^2
144+256 = c^2
400 = c^2
Take the square root of each side
sqrt(400) = sqrt(c^2)
20 = c
how do you solve literal eqations
Answer: When given a literal equation, you will often be asked to solve the equation for a
given variable. The goal is to isolate that given variable. The process is the same
process that you use to solve linear equations; the only difference is that you will
be working with a lot more letters, and you may not be able to simplify as much as
you can with linear equations. This packet will hopefully show you the process in a
simple manner so that you will be able to solve literal equations yourself.
Step-by-step explanation:
What factor is used to convert miles per minute to
miles per hour?
Answer:
The factor which is used to convert feet per minute into miles per minute is:
1 ft per minute=0.000189 miles per minute.
( since, 1 ft.= 0.000189 miles )
Step-by-step explanation:
This amount of chill is _ times the amount of cream cheese
Answer:
Is there supposed to be a picture?
Step-by-step explanation:
(1) Let T: Rn--->Rm be linear tranformations.
a. If T maps Rnonto Rm, give a relationship between m and n
b. If T is one-to-one, give a relationship between m and n
c. If T maps Rn onto Rm and is one-to-one, give a relationship between m and n
(Hint: Think about the size of the standard matrix representation of T and the placement of the pivots in each case)
(2) Let T: R3 ---> R4 be a linear transformation such that the only solution to T(x) = 0 is trivial solution.
a. If T is one-to-one
b. Does T map R3onto R4?
Justify your answers in each case.
(Hint:one way to approach this is to look at what the martix representation of T might look like and where it does or does not have pivots.)
(3) Suppose a linear transformation T: R2----> R2 is formed by taking a rotation counterclockwise of 90 degrees, follwed by a reflection through the X2-axis. Describe the points that will be moved back to their original position by this transformation?
(Hint: Think about what T will do to the unit box and the vectors e1 and e2)
Answer:
Check the explanation
Step-by-step explanation:
1.
(a)
n>=m
(b)
n <= m
(c)
n=m
2.
(a)
let T(v1) = T(v2)
=>
T(v1)-T(v2) = 0
=>
T(v1-v2) = 0
=>
v1-v2 = 0 from the hypothesis
=>
v1=v2
=>
T is one-one
thus proved
(b)
lets assume T is onto, we already know that T is one-one, so from above problem (third case where m=n)
we should have 3=4 which is impossible
so T is NOT onto.
3.
we need to find a,b such that
T(a,b) =(a,b)
=>
a= b
=>
points on the line x=y are the required points
Graph the system of equations on your graph paper to answer the question. {y=−x+3 y=x+5 What is the solution for this system of equations? Enter your answer in the boxes.
Answer:
(x,y) = (-1,4)
Step-by-step explanation:
y = y right? So all you have to do is replace both of the equations.
[tex]-x+3=x+5\\-x-x=5-3\\-2x=2\\x=-1[/tex]
after you've found the value of x just substitute it into ANY of these two equations!
For example if we get the first one we have
[tex]y=-(-1)+3\\y=1+3\\y=4[/tex]
And there you have it. Hope it helps!
what is the volume of a square pyramid with base edges 24 feet and slant height 37
7140 ft^3
6950 ft^3
6720 ft^3
7268 ft^3
The volume of a square pyramid with base edges of 24 feet and a slant height of 377268 feet is 74,182,973,440 cubic feet.
Explanation:The volume of a square pyramid can be found using the formula: volume = (1/3) * base area * height. In this case, the base of the pyramid is a square with edges measuring 24 feet, so the base area is
= 24 * 24
= 576 square feet.
The slant height of the pyramid is given as 377268 ft^3, but the units should be in feet, not ft^3, as ft^3 represents volume. Therefore, it is likely a typo.
Assuming the slant height is actually 377268 feet, we can use the Pythagorean theorem to find the height of the pyramid.
The height is given by
[tex]h = \sqrt{(slant height^2 - (base edge/2)^2)[/tex]
[tex]= \sqrt{(377268^2 - (24/2)^2)[/tex]
[tex]= \sqrt{(142288127824 - 144)[/tex]
= 377268 feet.
Now we can calculate the volume using the formula: volume
= (1/3) * 576 * 377268
= 74,182,973,440 cubic feet.
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Put these fractions in order from least to greatest. 3/12 1/6 2/3
Answer:1
1/6 3/12 2/3
Step-by-step explanation:
3/12 = 2/6
2/3 = 4/6
1/6<2/6<2/3
Answer:
The answer is 3/12 1/6 2/3
Step-by-step explanation:
The reason why is because the denominator is larger than the rest. The larger the denominator the smaller the number. For example: 2/13 is less than 4/6 because the denominator is bigger. Now if it were 6/12 and 1/2 it would be equal since 6 is half of 12. Hope this helped!
Ri’Hanna has n nickels. Shania has 4 times as many nickels as Ri’Hanna has. Write an expression for the total number of nickels Ri’Hanna and Shania have. SImplify the Expression.
Answer:
5n
Step-by-step explanation:
i think
To find the total number of nickels Ri’Hanna and Shania have together, add the number of nickels Ri’Hanna has (n) and the number of nickels Shania has (4n). The simplified expression is 5n.
Explanation:Ri’Hanna has n nickels, and Shania has 4 times that amount. This could be represented by the expression 4n. To calculate the total number of nickels they have together, you add the amount of nickels Ri’Hanna has (n) and the amount Shania has (4n). So, the expression representing the total nickels is n + 4n. When you add n + 4n, it simplifies to 5n.
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A Cell Phone company sells cellular phones and airtime in a State. At a recent meeting, the marketing manager states that the average age of the customers is 40 years. Before actually completing the advertising plan, it was decided to select a random sample of customers. Among the questions asked in the survey of 50 customers was the customer’s ages. The mean and the standard deviation of the data based on the survey are 38 years and 7 years. a. Formulate a hypothesis to test the marketing manager’s claim. b. Does the sample support manager’s claim. Test at 0.05 level of significance.
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that the average age of the customers differs from 40 years.
The sample does not support the manager claim (the average age seems to differ from 40 years).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The manager claims that the average age of customers is 40 years. As this is an equality, we will test if the average age differs from 40. If the null hypothesis failed to be rejected, the claim of the manager is right.
Then, the claim is that the average age of the customers differs from 40 years.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=40\\\\H_a:\mu\neq 40[/tex]
The significance level is 0.05.
The sample has a size n=50.
The sample mean is M=38.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{7}{\sqrt{50}}=0.99[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38-40}{0.99}=\dfrac{-2}{0.99}=-2.02[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
This test is a two-tailed test, with 49 degrees of freedom and t=-2.02, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t<-2.02)=0.049[/tex]
As the P-value (0.049) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average age of the customers differs from 40 years.
Assume that the volume of air in an average adult’s lung follows a transformed sine function, as function of time t in seconds,
V (t) = A + B sin(ωt)
Below is a table of measurements of the volume. Identify constants A, B, and ω so that the function above fits these measurements. After 12 seconds, the measurements will repeat.
t - 0 3 6 9 12
V(t) - 7 9 7 5 7
Answer:
Step-by-step explanation:
Given that,
v(t) = A + B•sin(ωt)
Then,
When t = 0 v(t)= 7
7 = A + B•Sin(ω×0)
7 = A + B•Sin0
7 = A
Then,
A = 7
v = 7 + B•sin(ωt)
So,
When t = 3, v(t) = 9
v = A + B•sin(ωt)
9 = 7 + B•Sin(3w)
9-7 = B•sin(3ω)
B•sin(3w) = 2. Equation 1
Also, at t = 6 v(t) = 7, at this point, when it returns back to7, it has complete one oscillation
v = A + B•sin(ωt)
7 = 7 + B•Sin(6w)
7-7 = B•sin(6ω)
B•sin(6w) = 0
Sin(6w) = 0 / B
Sin(6w) = 0
Take arcsin of both sides
6w = Sin~1(0)
6w = π, since it has complete one oscillation
Then, w = π /6
w = π/6
Then,
v(t) = 7 + B•Sin(πt/6)
From equation 1
B•sin(3w) = 2.
B•Sin(3 × π/6) = 2
B•Sin(½π) = 2
B = 2
Then,
v(t) = A + B•sin(ωt)
A = 7, B = 2 and w = π/6
v(t) = 7 + 2•sin(πt/6)
7-7(5+x)-9x in simplified
Answer:
-28 - 16x
Step-by-step explanation:
7-7(5+x)-9x
Distribute
7 - 35 -7x -9x
Combine like terms
-28 - 16x
The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 5.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]
Test statistic t=-0.256
P-value = 0.4
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that that smartphone carrier's data speeds at airports is less than 5 mbps.
Step-by-step explanation:
The question is incomplete:
Sample mean (M): 4.79
Sample STD (s): 5.8
Sample size (n): 50
This is a hypothesis test for the population mean.
The claim is that that smartphone carrier's data speeds at airports is less than 5 mbps.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]
The significance level is 0.05.
The sample has a size n=50.
The sample mean is M=4.79.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.8}{\sqrt{50}}=0.82[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.79-5}{0.82}=\dfrac{-0.21}{0.82}=-0.256[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
This test is a left-tailed test, with 49 degrees of freedom and t=-0.256, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-0.256)=0.4[/tex]
As the P-value (0.4) is bigger 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 that smartphone carrier's data speeds at airports is less than 5 mbps.
A software company decided to conduct a survey on customer satisfaction. Out of 564 customers who participated in the online survey, 51 rated the overall services as poor. Test, at level , the null hypothesis that the proportion of customers who would rate the overall car rental services as poor is 0.1 versus a two-sided alternative. Find the value of the test statistic (round off to first decimal place).
Answer:
[tex]z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8[/tex]
[tex]p_v =2*P(z<-0.760)=0.447[/tex]
Step-by-step explanation:
Information given
n=564 represent the sample selected
X=51 represent the number of people who rated the overall services as poor
[tex]\hat p=\frac{51}{564}=0.0904[/tex] estimated proportion of people who rated the overall services as poor
[tex]p_o=0.1[/tex] is the value to compare
z would represent the statistic
Hypothsis to analyze
We want to analyze if the proportion of customers who would rate the overall car rental services as poor is 0.1, so then the system of hypothesis are:
Null hypothesis:[tex]p=0.1[/tex]
Alternative hypothesis:[tex]p \neq 0.1[/tex]
The statistic for a one z test for a proportion is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8[/tex]
And the p value since we have a bilateral test is given b:
[tex]p_v =2*P(z<-0.760)=0.447[/tex]
The question is about testing a null hypothesis in a customer satisfaction survey for a software company. The null hypothesis is that 10% of customers would rate the services as poor. The calculated test statistic was approximately -1.3.
Explanation:
The question involves testing a null hypothesis regarding the proportion of customers who would rate the software company's services as poor. We are given that a total of 564 customers took part in the survey, out of which 51 rated the services as poor. Here, the null hypothesis is that 10% (or 0.1) of customers would rate the services as poor.
To test the null hypothesis, we compare the sample proportion to the claimed proportion (0.1). The sample proportion in this case is 51/564 = 0.0904. We can calculate the test statistic using the formula for sample proportion, which is (p' - p) / sqrt [ p * (1 - p) / n ], where p is the claimed proportion, p' is the sample proportion, and n is the sample size. In this case, the test statistic would be approximately (0.0904 - 0.1) / sqrt [0.1 * (1 - 0.1) / 564] = -1.3 (rounded to the first decimal).
The p-value corresponds to the test statistic under the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis. But here, we didn't calculate the p-value as it wasn't part of the question, so we won't make a decision on the null hypothesis.
Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
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A survey was taken of randomly selected Americans, age 65 and older, which found that 401 of 1020 men and 536 of 1059 women suffered from some form of arthritis. a) Are the assumptions and conditions necessary for inference satisfied? Explain. b) Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. c) Interpret your interval in this context. d) Does this suggest that arthritis is more likely to afflict women than men? Explain.
Final answer:
The assumptions and conditions necessary for inference are satisfied, and a 95% confidence interval can be created to estimate the difference in proportions of senior men and women with arthritis. The interval provides a measure of precision, and the results do not suggest that arthritis is more likely to afflict women than men.
Explanation:
a) The assumptions and conditions necessary for inference are satisfied. Random sampling was used to select Americans age 65 and older, which helps ensure representativeness. The sample sizes are also large enough for accurate analysis.
b) To create a 95% confidence interval for the difference in proportions, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2))
c) The 95% confidence interval indicates that we are 95% confident that the true difference in proportions falls within the given range. It provides a measure of the precision of our estimate.
d) The survey results do not suggest that arthritis is more likely to afflict women than men. The confidence interval encompasses a range of values, indicating that the difference in proportions could be quite small or even favor men.
Yes, it was a random sample less than 10% of the population was sampled the groups were independent, and there were more than 10 successes and failures in each group option(D). The confidence interval for the difference in proportions (p₁ - p₂) is approximately (4.8%, 13.2%) after rounding to three decimal places as needed. The proportion of American women, age 65 and older, who suffer from arthritis is between 4.8% and 13.2% higher than the proportion of American men of the same age who suffer from arthritis. Therefore, arthritis is more likely to afflict women than men.
Yes, the entire interval lies above 0 option(C).
The assumptions and conditions necessary for inference in parts (a), (b), (c), and (d) can be evaluated as follows:
(a) The conditions for inference include:
The sample must be random.The sample size must be less than 10% of the population.The groups must be independent.There must be at least 10 successes and 10 failures in each group.Given the survey data:
It is a random sample.Both samples are less than 10% of their respective populations.The groups are independent.There are more than 10 successes and 10 failures in each group.Therefore, the correct answer is D. Yes, it was a random sample less than 10% of the population was sampled the groups were independent, and there were more than 10 successes and failures in each group.
(b) To create a 95% confidence interval for the difference in proportions of senior men and women who have arthritis, we follow these steps:
Calculate the sample proportions:⇒ p₁ = 532 ÷ 1065 and
⇒ p₂ = 418 ÷ 1019.
Find the standard error (SE) of the difference between proportions:⇒ SE = √((p₁(1 - p₁) ÷ n₁) + (p₂(1 - p₂) ÷ n₂))
Calculate the margin of error (ME) using the Z-score for a 95% confidence level (Z = 1.96):⇒ ME = Z × SE
Determine the confidence interval:= (p₁ - p₂) ± ME
The confidence interval for the difference in proportions (p₁ - p₂) is approximately (4.8%, 13.2%) after rounding to three decimal places as needed.
(c)There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between 4.8% and 13.2% higher than the proportion of American men of the same age who suffer from arthritis.
(d) Since the entire confidence interval lies above 0, it suggests that senior women are more likely to suffer from arthritis. The correct answer is C. Yes, the entire interval lies above 0.
Complete question:
A survey was taken of randomly selected Americans, age 65 and older, which found that 418 of 1019 men and 532 of 1065 women suffered from some form of arthritis.
a) Are the assumptions and conditions necessary for inference satisfied? Explain.
A. No, more than 10% of the population was sampled. ?
B. No, the groups were not independent.
C. No, it was not a random sample.
D. Yes, it was a random sample less than 10% of the population was sampled the groups were independent, and there were more than 10 successes and failures in each group.
b) Let p₁ be the sample proportion of senior women suffering from some form of arthritis, and let p₂ be the sample proportion of senior men suffering from some form of arthritis. Create a 95% confidence interval for the difference in proportions of senior men and women who have this disease, p₁ - p₂.
The confidence interval is
( Round to three decimal places as needed.)
c) There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between % and % than the proportion of American men of the same age who suffer from arthritis.
(Round to one decimal place as needed.)
d) Does this suggest that arthritis is more likely to afflict women than men? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
A. No, the interval is too close to 0.
B. Yes, there is 95% confidence, based on these samples that about % of senior women suffer from arthritis, while only % of senior men suffer from arthritis.
(Round to one decimal place as needed.)
C. Yes, the entire interval lies above 0.
D. No, a conclusion cannot be made based on the confidence interval.
Connor earned $85 at his job when he worked for 10 hours. What was his hourly pay rate in dollars per hour?
Answer:
8.5$
Step-by-step explanation:
85 diveded by 10 is 8.5$.
Answer:
Connor's hourly pay rate is $8.50
Step-by-step explanation:
Think of it as finding the unit rate.
hours : dollars
10 : 85
1 : ?
Since you must divide by 10 to get from 10 to 1, you must do the same for the other side, so you do 85 divided by 10.
85 / 10 = 8.5
Therefore, Connor's hourly pay rate is $8.50.
What is the degree and the polynomial term?
Answer:
choice A is the best 2nd degree, trinomial
Step-by-step explanation:
-x^2 +3x - 4
has 3 unique terms which make it a trinomial
The highest degree is 2 since the the highest valued exponent is 2
Suppose two players are playing a game, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then Even keeps both pennies, so wins one from Odd ( 1 for Even, -1 for Odd). If the pennies do not match (one heads and one tails) Odd keeps both pennies, so receives one from Even (-1 for Even, 1 for Odd).
1. Please draw the payoff matrix for this game.
2. Does Even have a dominant strategy?
Answer:
1.
E(down) / Odd(Across) H T
H (1,-1) (-1,1)
T (-1,1) (1,-1)
2. Even doesn't have a dominant strategy as both the strategies are providing equal payoffs for pure strategy.