Question

In the dataset StudentSurvey, 361 students recorded the number of hours of television they watched per week. The average is 2 = 6.504 hours with a standard deviation of 5.584. Does this provide evidence that college students at this university watch more 5 hours of television per week? Clearly show all details of the hypothesis test: State the hypotheses for the test, calculate the test statistic, find the p-value, state the conclusion of the test, Reject or Do Not Reject, if we assume a 5% significance level, and state this conclusion in context. Round to three decimal places if needed.

Answer 1

To determine if college students at this university watch more than 5 hours of television per week, we will conduct a hypothesis test using the given data. The null hypothesis is that the average is less than or equal to 5 hours, while the alternative hypothesis is that the average is greater than 5 hours. We will calculate the test statistic, find the p-value, and compare it to the significance level to make a decision.

Step-by-step explanation:

In order to determine whether college students at this university watch more than 5 hours of television per week, we will conduct a hypothesis test.

Null Hypothesis (H0): The average number of hours of television watched by college students at this university is less than or equal to 5 hours per week.

Alternative Hypothesis (Ha): The average number of hours of television watched by college students at this university is greater than 5 hours per week.

To test this hypothesis, we will calculate the test statistic using the sample mean, population mean, sample standard deviation, and sample size.

1. Test Statistic (z-score) = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(Sample Size)).
2. Calculate the z-score using the given values: z = (6.504 - 5) / (5.584 / sqrt(361)).
3. Calculate the p-value associated with the test statistic using a standard normal distribution table or a statistical software.
4. Compare the p-value to the significance level (0.05) to make a decision.

If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is evidence that college students at this university watch more than 5 hours of television per week. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that college students at this university watch more than 5 hours of television per week.

Based on the results of the hypothesis test, we can make a conclusion in context with the given question.