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

Question

A credit card company claims that the mean credit card debt for individuals is greater than $ 5 comma 100. You want to test this claim. You find that a random sample of 38 cardholders has a mean credit card balance of $ 5 comma 243 and a standard deviation of $ 600 . At alpha equals 0.05 , can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a . Which of the following correctly states Upper H 0 and Upper H Subscript a ? A. Upper H 0 : mu greater than$5 comma 100Upper H Subscript a : mu less than or equals$5 comma 100 B. Upper H 0 : mu greater than or equals$5 comma 100Upper H Subscript a : mu less than$5 comma 100 C. Upper H 0 : mu less than or equals$5 comma 100Upper H Subscript a : mu greater than$5 comma 100 D. Upper H 0 : mu equals$5 comma 100Upper H Subscript a : mu greater than$5 comma 100 E. Upper H 0 : mu greater than$5 comma 100Upper H Subscript a : mu less than or equals$5 comma 100 F. Upper H 0 : mu equals$5 comma 100Upper H Subscript a : mu not equals$5 comma 100 (b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s), t 0 ? t 0 equalsnothing (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.) A. tless than nothing and tgreater than nothing B. tless than nothing C. nothing less thantless thannothing D. tgreater than nothing (c) Find the standardized test statistic t. tequals 1.47 (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. A. Fail to reject Upper H 0 because the test statistic is not in the rejection region. B. Reject Upper H 0 because the test statistic is not in the rejection region. C. Fail to reject Upper H 0 because the test statistic is in the rejection region. D. Reject Upper H 0 because the test statistic is in the rejection region. (e) Interpret the decision in the context of the original claim. A. At the 5 % level of significance, there is sufficient evidence to support the claim that the mean credit card debt is less than $5 comma 100 . B. At the 5 % level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is greater than $5 comma 100 . C. At the 5 % level of significance, there is sufficient evidence to support the claim that the mean credit card debt is greater than $5 comma 100 . D. At the 5 % level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is less than $5 comma 100 .

Explanation / Answer

Given that,
population mean(u)=5100
sample mean, x =5243
standard deviation, s =600
number (n)=38
null, Ho: <5100
alternate, H1: >5100
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.687
since our test is right-tailed
reject Ho, if to > 1.687
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =5243-5100/(600/sqrt(38))
to =1.469
| to | =1.469
critical value
the value of |t | with n-1 = 37 d.f is 1.687
we got |to| =1.469 & | t | =1.687
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :right tail - Ha : ( p > 1.4692 ) = 0.07512
hence value of p0.05 < 0.07512,here we do not reject Ho
ANSWERS
---------------
null, Ho: <=5100
alternate, H1: >5100
test statistic: 1.469
critical value: 1.687
decision: do not reject Ho
p-value: 0.07512

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