Page 11 of 14 31. Two lots of logs are known to be infested by bark beetles. If 10 out of 45 logs examined were infested in Lot 1, and 12 out of 40 in Lot 2... [*Exercise 8.15] a) Find the 90% and 95% confidence intervals for the proportion of infested logs in Lot 2. b) Are the levels of infestation significantly different in the two lots? (use a hypothesis test at = 0.01) c) Find the 99% confidence interval for the difference between proportions of infested logs in the two lots. Compare the results to Q 31 (b). d) How large a sample size is needed to be 95% confident that the sample proportion in Lot 2 will be within 1% of the true fraction of infested logs?