Exam 18: More About Tests

Health Canada reports that,in 2005,85% of Canadians were satisfied with the health care services they received.Suppose you wish to conduct a hypothesis test to determine if there is now a smaller percentage of Canadians are satisfied with the health care services they received.Identify the Type I error in this context.

A professional basketball player with a poor free throw percentage gets a personal coach to help him increase his percentage.He tells his coach that he has raised his proficiency from 70% to 90%.To see whether the athlete has improved,the coach asks the athlete to take 10 shots.He hits 10 out of 10.Suppose the athlete really is no better than before (still a 70% shooter).What's the probability that he could hit at least 10 out of 10 shots anyway?

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 6.1%.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluated its retention rate.Identify the Type I error in this context.

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese; that is,they had a body mass index (BMI)of 30 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004.To test your belief,take a random sample of 1000 Canadians.If you plan to perform the test at α = 0.05 and the true percentage of obese Canadians is currently 24.8%,what is the power of the test?

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy to see if it's better.What are the null and alternative hypotheses?

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better and receives a P-value of 0.06.What is reasonable to conclude about the new strategy using α = 0.05?