A credit card company claims that the mean credit card debt for individuals is greater than $5,100. You want to test this claim. You find that a random sample of 32 cardholders has a mean credit card balance of $5,242 and a standard deviation of$575. At a = 0.01, can you support the claim? Complete parts (a) through (d) below. Assume the population is normally distributed.(a) Write the claim mathematically and identify Ho and H2.Which of the following correctly states H, and H,?O A. Ho: µ> $5,100Ha: us $5,100В. Но: и- $5,100Hai µ > $5,100С. Но: 3 $5,100Ha: u# $5,100O D. Ho: µ2 $5,100Ha:u< $5,100O E. Ho: µ> $5,100Ha: us $5,100Ο F H0: μS $5,1 00Ha: µ > $5,100(b) Find the critical value and identify the rejection region.What is the critical value, to?to =0(Use a comma to separate answers as needed. Round to three decimal places as needed.)Determine the rejection region. Select the correct choice below and fill in the ansswer box within your choice.(Round to three decimal places as needed.)O A. t<В. t<and t>O C. t>D. (d) Decide whether to reject or fail to reject the null hypothesis.O A. Reject H, because the test statistic is not in the rejection region.B. Reject Ho because the test statistic is in the rejection region.O C. Fail to reject H, because the test statistic is not in the rejection region.D. Fail to reject Ho because the test statistic is in the rejection region.

In this question we use one sample t test and find the following parts.In this question we are given that , sample mean =$5242 standard deviation = $ 575 sample size = n= 32 claimed mean= $5100 We use t test for the above data at 0.01 level df= n-1 = 32-1= 31 t(31,0.01)= 2.453t critical value at 0.01 = 2.453 a) H0: μ≤5100 H1: μ>5100b) t critical value at 0.01 = 2.453Rejection region= Reject H0 when it is true μ>5100 is the rejection regionRejection region in terms of t:t>2.453c) tcal= x¯-μσn ~tn-1tcal=5242-510057532tcal= 1.39 standardized value of t(31,0.01) = 1.39 d) t calculated value is less than tabulated value, hence we reject null hypothesis because test statistic lies in the rejection region.

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Statistics

-0.01, can you support the claim? Complete parts (a) through (d) below. Assume the popul distributed. Vrite the claim mathematically and identify Ho and H ch of the following correctly states Ho and H,? О В. Но: и $5,100 H:u> $5,100 OC. Ho: u= $5,100 Hiu#$5,100 A. Họ: u> $5,100 Hius $5,100 p. Ho: u2 $5,100 Hiu< $5,100 OF. Ho: us$5,100 O E. Ho: u> $5,100 Hius $5,100 H:u> $5,100 ind the critical value and identify the rejection region. t is the critical value, to? a comma to separate answers as needed. Round to three decimal places as needed.) rmine the rejection region. Select the correct choice below and fill in the answer box within your choice. and to three decimal places as needed.) A. t< O B. t< and t> t> OD.

-0.01, can you support the claim? Complete parts (a) through (d) below. Assume the popul distributed. Vrite the claim mathematically and identify Ho and H ch of the following correctly states Ho and H,? О В. Но: и $5,100 H:u> $5,100 OC. Ho: u= $5,100 Hiu#$5,100 A. Họ: u> $5,100 Hius $5,100 p. Ho: u2 $5,100 Hiu< $5,100 OF. Ho: us$5,100 O E. Ho: u> $5,100 Hius $5,100 H:u> $5,100 ind the critical value and identify the rejection region. t is the critical value, to? a comma to separate answers as needed. Round to three decimal places as needed.) rmine the rejection region. Select the correct choice below and fill in the answer box within your choice. and to three decimal places as needed.) A. t< O B. t< and t> t> OD.

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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Question

A credit card company claims that the mean credit card debt for individuals is greater than $5,100. You want to test this claim. You find that a random sample of 32 cardholders has a mean credit card balance of $5,242 and a standard deviation of
$575. At a = 0.01, can you support the claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
(a) Write the claim mathematically and identify Ho and H2.
Which of the following correctly states H, and H,?
O A. Ho: µ> $5,100
Ha: us $5,100
В. Но: и- $5,100
Hai µ > $5,100
С. Но: 3 $5,100
Ha: u# $5,100
O D. Ho: µ2 $5,100
Ha:u< $5,100
O E. Ho: µ> $5,100
Ha: us $5,100
Ο F H0: μS $5,1 00
Ha: µ > $5,100
(b) Find the critical value and identify the rejection region.
What is the critical value, to?
to =
0
(Use a comma to separate answers as needed. Round to three decimal places as needed.)
Determine the rejection region. Select the correct choice below and fill in the ansswer box within your choice.
(Round to three decimal places as needed.)
O A. t<
В. t<
and t>
O C. t>
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 H, because the test statistic is not in the rejection region.
B. Reject Ho because the test statistic is in the rejection region.
O C. Fail to reject H, because the test statistic is not in the rejection region.
D. Fail to reject Ho because the test statistic is in the rejection region.

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