PLEASE ANSWER QUESTION 8, I AM ONLY POSTING QUESTION 7 AS A REFERENCE THANK YOU.

7. In a study of insect physiology, eggs from a beneficial species of moth were put in boxes placed in chambers at different temperatures. There were 30 eggs placed into each box, and the number of eggs hatching after 30 days were counted. The first box at 10C had 0 hatch, the first box at 15C had 1 hatch, and the first box at 20C had 25 hatch. The data is courtesy of Jim Nechols, Department of Entomology, Kansas State University. (a) Construct appropriate confidence intervals for the probability that an egg hatches at each temperature. (b) Assess informally whether the probabilities could be the same at each temperature. Explain your reasoning. Note that we will develop more formal ways of making these comparisons in Chapter 2.

8. Continuing Exercise 7, the researchers actually used 10 different boxes of 30 eggs at each temperature. The counts of hatched eggs for the 10 boxes at 15C were 1, 2, 4, 1, 0, 0, 0, 12, 0, and 2. (a) Why do you suppose that the researchers used more than one box at each temperature? (b) Construct appropriate confidence intervals for the probability that an egg hatches in each box. (c) Based on the intervals, does it appear that the probability that an egg hatches is the same in all boxes? Explain your reasoning. (d) All 10 boxes were held in the same chamber at the same time, and the chamber was set to 15C. How do you suppose it could happen that they give such different counts? Hint: See part (c). (e) Do you think that it would be appropriate to consider the data as w = 22 successes coming from a binomial distribution with n = 300 trials? Why or why not?