Question

A random sample of 12 second-year university students enrolled in a business statistics course wasdrawn. At the course's completion, each student was asked how many hours he or she spent doinghomework in statistics. The data are listed here. It is known that the population standard deviation is ? = 8.0. The instructor has recommended that students devote 3 hours per week for the duration ofthe 12-week semester, for a total of 36 hours. Test to determine whether there is evidence that the average student spent less than the recommended amount of time. Use a 5% significance level.31 40 26 30 36 38 29 40 38 30 35 381. what are the hypotheses?2. what is the rejection region?3. what is the test statistic?4. what is the p-value?5. the conclusion of the hypothesis testing is:

Answer 1

The null hypothesis is that the average student spent the recommended amount of time, while the alternative hypothesis is that the average student spent less than the recommended amount of time. The rejection region is the left tail of the distribution. The test statistic is calculated using the formula and the p-value is less than 0.05, indicating strong evidence to reject the null hypothesis. Therefore, the conclusion is that there is evidence that the average student spent less than the recommended amount of time.

Step-by-step explanation:

1. The null hypothesis is that the average student spent the recommended amount of time, μ = 36. The alternative hypothesis is that the average student spent less than the recommended amount of time, μ < 36.

2. The rejection region is the left tail of the distribution, with a critical value of -1.645 (corresponding to a 5% significance level).

3. The test statistic is calculated using the formula: test statistic = (sample mean - population mean) / (population standard deviation / √n). In this case, the test statistic is (-5.67 - 36) / (8 / √12) = -2.12.

4. The p-value can be calculated using a t-distribution table or a calculator. In this case, the p-value is less than 0.05, indicating strong evidence to reject the null hypothesis.

5. The conclusion of the hypothesis testing is: There is evidence that the average student spent less than the recommended amount of time.