Question

In a study entitled How Undergraduate Students Use Credit Cards, it was reported that undergraduate students have a mean credit card balance of $3173 (Sallie Mae, April 2009). This figure was an all-time high. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, use a population standard deviation σ= $1000.

State the null and alternative hypotheses.

What are the test statistics for a sample of 180 undergraduate students with a sample mean credit card balance of $3325?

What is the p-value?

At α =.05, what is your conclusion?

At α =.01, what is your conclusion?

Answer 1

Null and alternative hypotheses

Ho : = 3173

H1 : > 3173

Test statistic

Z = ( xbar - )/(/√n) = ( 3325 - 3173)/(1000/√180)

Test statistic Z = 2.04

p-value for Z = 2.04 and right tailed test

p-value = P( Z > 2.04)

p-value = 0.0207

Decision rule : we reject the null hypothesis if p-value < a ( level of significance) otherwise we fail to reject the null hypothesis

At a = 0.05 , p-value = 0.0207 < 0.05

Conclusion : Reject the null hypothesis , there is sufficient evidence to support the claim that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report

At a = 0.01 , p-value > 0.01

Conclusion : Fail to reject the null hypothesis , there is no sufficient evidence to support the claim that the the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report