A recent national survey found that high school students watched an average mean of 8 DVDs per month with a population standard deviation of 5 hours A random sample of 36 college students revealed tha

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