1) Sneeze According to work done by Nick Wilson of Otago University Wellington, the proportion of individuals who cover their mouth when sneezing is 0.733. As part of a school project, Mary decides to confirm the work of Professor Wilson by observing 100 randomly selected individuals sneeze and finds that 78 covered their mouth when sneezing.
(a) What are the null and alternative hypotheses for Mary's project?
(b) Verify the requirements that allow use of the normal model to test the hypothesis are satisfied.
(c) Does the sample evidence contradict Professor Wilson's findings?
2) Pharmaceuticals A pharmaceutical company manufactures a 200-milligram (mg) pain reliever. Company specifications require that the standard deviation of the amount of the active ingredient must not exceed 5 mg. The quality-control manager selects a random sample of 30 tablets from a certain batch and finds that the sample standard deviation is 7.3 mg. Assume that the amount of the active ingredient is normally distributed. Determine whether the standard deviation of the amount of the active ingredient is greater than 5 mg at the α = 0.05 level of significance.
3) To test H0: p = 0.40 versus H1: p > 0.40, a simple random sample of n = 200 individuals is obtained and x = 84 successes are observed.
(a) What does it mean to make a Type H error for this test?
(b) If the researcher decides to test this hypothesis at the α = 0.05 level of significance, compute the probability of making a Type II error if the true population proportion is 0.44. What is the power of the test?
(c) Redo part (b) if the true population proportion is 0.47.
4) Infidelity According to menstuff.org, 22% of married men have "strayed" at least once during their married lives. A slog of 500 married men results in 122 indicating that they have strayed at least once during their married life. Does this survey result contradict the results of menstuff.org?
5) Studying Enough? It is suggested by college mathematics instructors that students spend 2 hours outside class studying for every hour in class. So, for a 4-credit-hour math class, students should spend at least 8 hours (480 minutes) studying each week. The given data, from Michael Sullivan's College Algebra class, represent the time spent on task recorded in MyMathLab (in minutes) for randomly selected students during the third week of the semester. Determine if the evidence suggests students may not, in fact, be following the advice. That is, does the evidence suggest students are studying less than 480 minutes each week? Use α = 0.05 level of significance. Note: A normal probability plot and boxplot indicate that the data come from a population that is normally distributed with no outliers.
6) Effect of a Redo Problem 3(b) with a = 0.01. What effect does lowering the level of significance have on the power of the test? Why does this make sense?