COC Math 140 Two-Proportion Hypothesis Testing Practice Problems

COC Math 140 Two-Proportion Hypothesis Testing Practice Problems

Perform an hypothesis test for each of the following. Be sure to (1) state your null and alternative hypotheses & define your parameters; (2) write your conclusion, which mustinclude your decision (in terms of the null hypothesis), alpha level, p-value, and context (in terms of the alternative hypothesis). You may assume that conditions have been met and checked.

1. Do younger people use online instant messaging (IM) more often than older people? A random sample of IM users found that 73 of the 158 people in the sample aged 18 to 27 said they used IM more often than email. In the 28-39 age group, 26 of 143 people used IM more often than email. Is there a significant difference between the population proportions (i.e., do all younger people use online IM more often than older people)?

1. Is rap music more popular among young blacks than among young whites? A sample survey compared 634 randomly chosen blacks aged 15 to 25 with 567 randomly selected whites in the same age group. It found that 368 of the blacks and 130 of the whites listened to rap music every day. Does this data show that rap music is more popular among all young blacks than among all young whites? Use a 1% alpha level and conduct an hypothesis test.

1. A study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school seniors in Illinois. Results showed that 34 of the freshmen and 24 of the seniors had used anabolic steroids. Steroids, which are dangerous, are sometimes used to improve athletic performance. Does this data show that there is a significantly different proportion of freshmen using steroids than seniors using steroids. Carry out a 2-proportion hypothesis test at an alpha level of 0.05.

1. A study reported in the medical journal Fertility and Sterility sought to determine whether the ancient Chinese art of acupuncture could help infertile women become pregnant. One hundred sixty healthy women who planned to have IVF were recruited for the study. Half of the subjects (80) were randomly assigned to receive acupuncture 25 minutes before embryo transfer and again 25 minutes after the transfer. The remaining 80 women were assigned to a control group and instructed to lie still for 25 minutes after the embryo transfer. Of those 80 who received acupuncture, 34 got pregnant. Of the 80 who did not receive acupuncture (the control group), 21 got pregnant. Conduct a hypothesis test to determine if the pregnancy rate is higher for all women like these who received acupuncture. Use an alpha level of 1%.