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 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, use a population standard deviation σ=$1000.

a. State the null and alternative hypotheses.

Answer 1

The null hypothesis is that the mean credit card balance for undergraduate students is $3173, reflecting no increase from the April 2009 report. The alternative hypothesis is that the mean credit card balance has increased since then.

Step-by-step explanation:

To address the research question as to whether the mean credit card balance for undergraduate students has continued to increase since the April 2009 report, we establish the following hypotheses:

• The null hypothesis (H0): The mean credit card balance for undergraduate students has not increased since April 2009 and remains at $3173.
• The alternative hypothesis (H1): The mean credit card balance for undergraduate students has increased since April 2009, meaning it is greater than $3173.

In the context of hypothesis testing, the null hypothesis is a statement that there is no effect or no difference, and it is usually the hypothesis that researchers aim to challenge. The alternative hypothesis is what you might believe to be true or hope to prove true.

Given the assumption that previous studies used a population standard deviation (σ) of $1000, this will be a critical factor when performing the actual statistical test, such as a Z-test or T-test, depending on the sample size and other criteria of the study being conducted.