Question

In a study about undergraduate student credit card usage, 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 and had increased 44% over the previous five years. 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, assume a population standard deviation of 1800.

Suppose you look at a random sample of 192 undergraduate students with a sample mean credit card balance of $3536.7.

You wish to test the claim that the mean credit card balance is higher than it was in 2009 at the α=α=0.02 level.

What is the test statistic for this sample?
test statistic = (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value = (Report answer accurate to 4 decimal places.)

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 3173.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 3173.
• The sample data support the claim that the population mean is greater than 3173.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 3173.

Answer 1

The statistical software output for this problem is :

Test statistics = 2.800

P-value = 0.0026

The p-value is less than (or equal to) α .

reject the null

There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 3173.