Question

You wish to determine whether consumers have made substantial progress in reducing their credit card debt? Based on a sample of 1000 consumers in September 2001, and another sample of 1000 customers in September 2006, the average credit card debt 2711 in 2001 as compared to 2814 in 2006. The standard deviation of each sample was approximately 976. Using a level of significance of 0.1,

a. What are the null and alternative hypothesis? (How do yo know)

b. What is the critical value? (Explain and show work)

c. Which minitab output is appropriate for this problem? (How do you know)

d. What is your managerial conclusion? (why)

Answer 1

Claim : consumers have made substantial progress in reducing their credit card debt

Let µ₁ be the average credit card debt in September 2001 and µ₂ be the average credit card debt in September 2006

a) According to the claim  H₀: µ₁ = µ₂    vs H_a: µ₁ ≠ µ₂   

b) Critical value :

We are given α =0.1

degrees of freedom (df) = n₁+ n₂ - 2 = 1000 +1000 - 2 = 1998

Since H_a  contain  ≠ sign this is two tail test.

So we can find the critical value for α (two tail ) = 0.1 and and d.f = 1998 using t table .

Since d.f = 1000 is the last d.f on the table , we use it instead of 1998

Therefore critical value is 1.646

C) We can use Minitab to perform this test:

Go to Stat menu ---> Basic statistics ---> 2-sample t test.

d)

Critical region: Reject H₀, if | t | ≥ 1.646 Or fail to reject H0 , if |t| < 1.646

|t |is absolute value of t statistic.

Decision : we have t = -2.36 , so |t| = 2.36

As |t| > 1.646 we reject H₀

Conclusion : We have significant evidence that consumers have made substantial progress in reducing their credit card debt.