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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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