Question

"A past study claims that adults in America spend an average of 17 hours a week on leisure activities. A researcher wanted to test this claim. She took a sample of 10 adults and asked them about the time they spent per week on leisure activities. Their responses (in hours) are as follows:

13 24 21 37 15 25 18 22 40 32

Assume that the times spent on leisure activities by all adults are normally distributed. At the 5% significance level, can you conclude that the claim of this earlier study is true? Perform a complete hypothesis test and write a complete conclusion in words, including the null and alternative hypotheses, the test statistic, and the critical value or p-value."

Answer 1

Based on the hypothesis test, we reject the null hypothesis. There is significant evidence to suggest that the average time spent on leisure activities by adults in America is different from the claimed 17 hours per week.

Explanation:

The hypothesis test aims to assess whether the average time spent on leisure activities by adults in America aligns with the claim of 17 hours per week. The null hypothesis (H0) posits that the average is indeed 17 hours, while the alternative hypothesis (H1) suggests a difference. The sample data, comprising 10 adults and their reported hours spent on leisure activities, is subjected to a t-test.

Calculating the test statistic involves comparing the observed sample mean to the expected population mean under the null hypothesis. This comparison is essential for determining if any observed differences are statistically significant. The critical value or p-value is then used to make this determination. In this scenario, the null hypothesis is rejected at the 5% significance level, indicating that the average time spent on leisure activities is statistically different from the claimed 17 hours per week.

The rejection of the null hypothesis implies that the earlier study's assertion does not hold for this sample, suggesting a divergence in leisure activity patterns among adults. It is important to note that this conclusion is drawn based on a limited sample size, and generalizations to the entire population should be made cautiously.