Do College Students Watch Fewer DVDs Than High School Students? Hypothesis Test Results

To determine whether we can conclude that college students watch fewer DVDs per month than high school students, we need to conduct a hypothesis test.

Let's set up the null and alternative hypotheses:

Null hypothesis (H0): The mean number of DVDs watched by college students (μ) is equal to the mean number of DVDs watched by high school students (μ0). Alternative hypothesis (Ha): The mean number of DVDs watched by college students (μ) is less than the mean number of DVDs watched by high school students (μ0).

We will use a one-sample t-test to compare the sample mean of college students to the population mean of high school students.

Given: Population mean (μ0) = 8 DVDs per month Population standard deviation (σ) = 5 DVDs Sample size (n) = 36 Sample mean (x̄) = 7 DVDs per month

The test statistic for a one-sample t-test is given by: t = (x̄ - μ0) / (σ / √n)

Substituting the given values: t = (7 - 8) / (5 / √36) t = -1 / (5 / 6) t = -6 / 5

To determine the critical value for a one-tailed test at the 0.05 significance level, we look up the value in the t-distribution table for a sample size of 36 and a significance level of 0.05. The critical value is approximately -1.691.

Since the calculated t-value (-6/5) is less than the critical value (-1.691), we reject the null hypothesis.

Therefore, we can conclude that at the 0.05 significance level, college students watch fewer DVDs per month than high school students.