Do College Students Watch Fewer DVDs Than High School Students? A Statistical Analysis

To determine whether we can conclude that college students watch fewer DVDs per month than high school students, we can perform a hypothesis test.\n\nLet's define our null and alternative hypotheses:\n\nNull Hypothesis (H₀): The mean number of DVDs watched by college students is equal to the mean number of DVDs watched by high school students.\nAlternative Hypothesis (H₁): The mean number of DVDs watched by college students is less than the mean number of DVDs watched by high school students.\n\nWe can use a one-sample t-test to test the hypothesis. Since the population standard deviation is known, we can use the z-test formula for a sample mean.\n\nThe test statistic can be calculated using the formula:\n\nt = (sample mean - population mean) / (population standard deviation / √n)\n\nwhere:\nsample mean = 7 (from the sample of 36 college students)\npopulation mean = 8 (from the national survey of high school students)\npopulation standard deviation = 5\nn = 36\n\nPlugging in the values, we get:\n\nt = (7 - 8) / (5 / √36)\nt = -1 / (5 / 6)\nt = -1.2\n\nTo determine the critical value for a one-tailed test at the 0.05 significance level, we can consult the t-distribution table with 35 degrees of freedom (n-1). At a significance level of 0.05, the critical value is approximately -1.6909.\n\nSince the calculated t-value of -1.2 is not less than the critical value of -1.6909, we fail to reject the null hypothesis. There is not enough evidence to conclude that college students watch fewer DVDs per month than high school students at the 0.05 significance level.'}