1) Gregor Mendel discovered the basic laws of heredity by studying pea plants. In one experiment, he produced plants whose parent plants contained genes for both green and yellow pods. Mendel's theory states that the offspring of two such parents has probability 0.75 of having green pods.
a) You plant 16 pea plants. If Mendel is correct, you would expect 12 of them to have green pods. Suppose that 14 have green pods. Explain why you may NOT safely carry out a test of Ho:p=0.75 using this data
b) Suppose that 200 plants are produced and 160 of them have green pods. Explain why you CAN safely carry out a test of Ho:p=0.75 using this data
c) Carry out a two-sided test given the information in part (b). Does this data support or contradict Mendel's theory? Use a significance level of 5%, and include a conclusion.
2) Chantix is a drug used as an aid for those who want to stop smoking. The adverse reaction of nausea has been studied in clinical trials, and the table below summarizes results (based on data from Pfizer).
Treatment n X(number with insomnia)
Chantix 129 19
Placebo 805 13
Do the data suggest that people who use Chantix are significantly more likely to experience insomnia than people who are given a placebo?
a) Give the value of the pooled estimate of p for this test.
b) State your hypotheses, report the value of your test statistic, give the p-value of your test, and give a conclusion.
c) Give a 95% confidence interval estimate for the difference in population proportions and explain what it means.