Gender Differences in Relaxation Hours: Hypothesis Testing Using General Social Survey 2024

Step 1: Assumptions for Hypothesis Testing

Using the General Social Survey for 2018, you get a brief glimpse into gender differences in relaxation hours. The variable of interest is: “How many hours per day does respondent have to relax.” You decide to examine gender differences in the number of hours per day the respondent relaxes.

You hypothesize that men have a significantly higher mean number of relaxation hours per day in the population than women and decide to test your hypothesis at alpha = 0.05. 

Before you proceed: Based on the sig level of the Levene’s test in the SPSS output on page 2, what row will you use for further analysis? Bold your choice. 

a. Conduct a test of hypothesis using the five steps below:

Step 1

List the four assumptions that must be met before you can proceed with the test. Use notes!

Step 2

Write clear null and research hypotheses in notations and statements.

Step 3

i. Calculate the degrees of freedom (df) for this test (show your work)? Is it the same as the number in the “df” column on the next page?

ii. Using tail of the research hypothesis, alpha = 0.05 and df, what is the tcritical that sets up the critical or rejection region?

Step 4

i. Calculate the pooled standard error. Show the work to receive credit. Is it the same as the number in the “Std Error Difference” column on the next page? If not, recheck your calculations.

ii. Using the pooled standard error, calculate the test statistic or t-obtained. Is it the same as the number in the “t” column on the next page? If not, recheck your calculations.

iii. Using the SPSS output on the next page, report the p-value for the test statistic or tobtained. It’s the number in the “Sig (2-tailed)” column. 

Step 5

Based on the test statistic (or tobtained) and the p-value, state your final decision using the appropriate hypothesis and variables. (Use the example given in the lecture video to write a clear and specific decision.)

Finally, how does the 95% confidence interval in the SPSS output above support your final decision?