In a study entitled How Undergraduate Students Use Credit Cards, Sallie Mae repo
ID: 3361125 • Letter: I
Question
In a study entitled How Undergraduate Students Use Credit Cards, Sallie Mae reported that undergraduate students have a mean credit card balance of $3173. This figure was an all-time high and had increased 44% over the previous five years. Assume that a current study is being conducted to determine whether 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 -$1000. a. State the null and alternative hypotheses. b. What is the p-value for a sample of 180 undergraduate students with a sample mean 16. credit card balance of $3325? Using a.05 level of significance, what is your conclusion? c.Explanation / Answer
Solution:-
a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 3173
Alternative hypothesis: > 3173
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
b) Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 74.54
DF = n - 1
D.F = 179
t = (x - ) / SE
t = 2.04
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 2.04
Thus the P-value in this analysis is 0.02141
Interpret results. Since the P-value (0.02141) is less than the significance level (0.05), we have to reject the null hypothesis.