A credit card company claims that the mean credit card debt for individuals is greater than$5,300.You want to test this claim. You find that a random sample of37cardholders has a mean credit card balance of$5,509and a standard deviation of$575.Atα=0.01,can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. A credit card company claims that the mean credit card debt for individuals is greater than $5,300. You want to test this claim. You find that a randomsample of 37 cardholders has a mean credit card balance of $5,509 and a standard deviation of $575. At a = 0.01, can you support the claim? Completeparts (a) through (e) below. Assume the population is normally distributed.(a) Write the claim mathematically and identify H, and Ha.Which of the following correctly states H, and H,?OC. Ho: µ> $5,300O A. Ho: us $5,300Ha:u > $5,300O B. Ho: H2 $5,300Haiu< $5,300H3:us $5,300O D. Ho: H = $5,300Haiu > $5,300O E. Ho:H = $5300H:u = $5,300OF. Ho: H > $5,300Ha:us $5,300(b) Find the critical value(s) and identify the rejection region(s).What is(are) the critical value(s), to?to =O(Use a comma to separate answers as needed. Round to three decimal places as needed.)Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.(Round to three decimal places as needed.)O A. t<and t>O B. t<OC.(c) Find the standardized test statistic t.t =(Round to two decimal places as needed.)(d) Decide whether to reject or fail to reject the null hypothesis.O A. Reject Ho because the test statistic is not in the rejection region.B. Reject H, because the test statistic is in the rejection region.OC. Fail to reject Ho because the test statistic is not in the rejection region.O D. Fail to reject H, because the test statistic is in the rejection region.(e) Interpret the decision in the context of the original claim.O A. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is greater than $5,300.O B. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is less than $5,300.OC. At the 1% level of significance, there is sufficient evidence to support the claim that the mean credit card debt is greater than $5,300.O D. At the 1% level of significance, there is sufficient evidence to support the claim that the mean credit card debt is less than $5,300.

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Description: A credit card company claims that the mean credit card debt for individuals is greater than$5,300.You want to test this claim. You find that a random sample of37cardholders has a mean credit card balance of$5,509and a standard deviation of$575.Atα=0.

From the provided information, Sample size (n) = 37 Sample mean (x̅) = $5509 Sample standard…

Answered: A credit card company claims that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A credit card company claims that the mean credit card debt for individuals is greater than

$5,300.

You want to test this claim. You find that a random sample of

cardholders has a mean credit card balance of

$5,509

and a standard deviation of

$575.

α=0.01,

can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed.

A credit card company claims that the mean credit card debt for individuals is greater than $5,300. You want to test this claim. You find that a random
sample of 37 cardholders has a mean credit card balance of $5,509 and a standard deviation of $575. At a = 0.01, can you support the claim? Complete
parts (a) through (e) below. Assume the population is normally distributed.
(a) Write the claim mathematically and identify H, and Ha.
Which of the following correctly states H, and H,?
OC. Ho: µ> $5,300
O A. Ho: us $5,300
Ha:u > $5,300
O B. Ho: H2 $5,300
Haiu< $5,300
H3:us $5,300
O D. Ho: H = $5,300
Haiu > $5,300
O E. Ho:H = $5300
H:u = $5,300
OF. Ho: H > $5,300
Ha:us $5,300
(b) Find the critical value(s) and identify the rejection region(s).
What is(are) the critical value(s), to?
to =O
(Use a comma to separate answers as needed. Round to three decimal places as needed.)
Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.
(Round to three decimal places as needed.)
O A. t<
and t>
O B. t<
OC.
<t<
O D. t>
(c) Find the standardized test statistic t.
t =
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
O A. Reject Ho because the test statistic is not in the rejection region.
B. Reject H, because the test statistic is in the rejection region.
OC. Fail to reject Ho because the test statistic is not in the rejection region.
O D. Fail to reject H, because the test statistic is in the rejection region.
(e) Interpret the decision in the context of the original claim.
O A. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is greater than $5,300.
O B. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is less than $5,300.
OC. At the 1% level of significance, there is sufficient evidence to support the claim that the mean credit card debt is greater than $5,300.
O D. At the 1% level of significance, there is sufficient evidence to support the claim that the mean credit card debt is less than $5,300.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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