Exam 9: B: large-Sample Tests of Hypotheses

College Beach Volleyball Narrative A student government representative at a local university claims that 60% of the undergraduate students favour a move from court volleyball to beach volleyball`. A random sample of 250 undergraduate students was selected and 140 students indicated they favoured a move to beach volleyball. -Refer to College Beach Volleyball Narrative. Perform the appropriate test of hypothesis to test the representative's claim. Use = 0.05.

University Housing Costs Narrative A large university claims that the average cost of housing within 3 kilometres of the campus is $6900 per school year. A high school student is preparing her budget for her freshman year at the university. She is concerned that the university's estimate is too low. Having taken statistics, she decides to perform the following test of hypothesis: , where represents the average cost of housing per year within 3 kilometres of the university. -Refer to University Housing Costs Narrative. Describe the Type I error for this .

Nuclear Weapons Freeze Narrative A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze. -Refer to Nuclear Weapons Freeze Narrative. Set up the appropriate null and alternative hypotheses.

Red Meat Consumption Narrative To test the theory that the consumption of red meat in Canada has decreased over the past 10 years, a researcher decides to select hospital nutrition records for 400 subjects surveyed 10 years ago and to compare their average amount of beef consumed per year to amounts consumed by an equal number of subjects interviewed this year. The data are given in the table. -In an attempt to compare the starting salaries for graduates who majored in business and education, random samples of 50 recent graduates in each major were selected and the following information was obtained: Do the data provide sufficient evidence to indicate a difference in average starting salaries for graduates who majored in business and education? Test using

Business Graduates Earnings Narrative A professor claims that 70% of business graduates earn more than $45,000 per year. In a random sample of 300 graduates, 195 earn more than $45,000. -Refer to Business Graduates Earnings Narrative. Can we reject the professor's claim at the 5% significance level? Justify your conclusion.

Life Insurance Narrative An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000. -Refer to Life Insurance Narrative. Determine the critical region using a significance level = 0.05.