1. It is believed that introducing genetically modified mosquitos into a wild population of mosquitos will decrease their egg laying rates. To study this, the number of eggs produced by 16 egg laying moquitos were studied: 8 from a wild population and 8 from a population that had be mixed with the genetically modified mosquitos. The number of eggs produced by each mosquito are reported in the table below. Wild Population 35 19 32 46 28 24 36 42 Mixed Population 36 24 30 33 40 40 30 18 (a) What hypotheses do you suggest in order to test the claim above? (b) Test these hypotheses at level α = 0.05. Report the test you used, the value of the test statistic, the p-value of the test, and your interpretation of the results. (c) Are the hypotheses of the test you used satisfied by this data set? Defend your argument. 2. A study was performed to determine if either of two drugs significantly increase the rate of growth of hair in adult males. Six patients were given a placebo, eight patients received Treatment 1 (Drug A), and seven patients received Treatment 2 (Drug B). The growth rate of the patients hair was measured, and the results are reported in the table below. Observation # Control Treatment 1 Treatment 2 1 2 6.97 7.44 7.69 6.12 9.99 10.09 3 7.26 7.13 8.82 4 6.57 8.97 12.10 5 8.88 8.99 10.85 6 7 6.95 6.04 4.13 8.50 10.57 8 7.56 (a) Apply the F –test to this data set to test at level .05 to determine if the mean growth rate is the same across all 3 treatments. (b) Investigate all of the assumptions of the one way analysis of variance. Are they satisfied? Support your answer. (c) Apply Tukey’s Method to the data above to determine simultaneous confidence intervals for the diﬀerences between the three diﬀerent treatment means. Use these intervals to determine which means if any are significantly diﬀerent from the others at the .05 level.