Please show all the work so I know how to do it.

1) Recall the data on male fighter pilots and males from the general population from Homework 7. In the table below, we have the heights of 12 male fighter pilots and 14 males from the general public in inches. Both samples were randomly selected. The data file Pilot/General Heights is also available in our StatCrunch group. Assume the population of heights for fighter pilots and the general public follow normal distributions. Fighter Pilot Heights General Population Heights 65.3 68.9 67.5 67.4 68.3 71.4 66.6 71.2 63.7 73.0 69.6 69.3 67.7 73.2 64.9 64.9 68.0 73.1 64.8 74.2 68.2 81.2 66.2 62.7 65.2 63.8 Previously, we tested if the standard deviation of fighter pilot heights were less than 3 inches. Now, we will not assume the standard deviation of all males is 3 inches and will instead test if we have enough evidence to suggest that the standard deviation of fighter pilot heights is less than the standard deviation of the heights of males in the general population based only on the data given above. Use a = 0.05 to conduct the F test. Be sure to show each step of the test. Before beginning the test, in words and in the context of the problem, list the parameters of interest with the associated symbol.2) In a recent health survey, 340 randomly selected college undergraduates were asked, "Regarding your current weight, do you feel that you're: 'About right', 'Overweight', or 'Underweight'?" A contingency table summarizing the results of this survey is provided below. Assume that this is a representative sample for males and females in this age group. Questions are on the next page. About Right Overweight Underweight Total Female 218 25 5 248 Male 54 2 36 92 Total 272 27 41 340 9' What is the probability of selecting a person from the study that is male and feels underweight? b. What is the probability of selecting a female given that the person selected feels overweight? c. Conduct a full test for independence between sex and weight perception. Show all six steps. d. Based in the calculation for the test statistic in the hypothesis test, which weight perception had the largest source of dependence with sex? That is, which cell contributed the most to the test statistic? You may want to refer back to page 130 in Chapter 10 notes. 3) The data that follow are based on a study by Qa_r_|_e_y and j._a_ta_n_ (1969). The authors were interested in whether the presence of other people has an inuence on whether a person will help someone in distress. In this classic study, the experimenter (a female graduate student) had the subject wait in a room with 0, 2, or 4 other people. The experimenter announces that the study will begin shortly and walks into an adjacent room. In a few moments the person(s) in the waiting room hear her fall and complain of ankle pain. The dependent measure is the number of seconds it takes the subject to help the experimenter. The data are given below: 0 People Present 2 People Present 4 People Present 25 30 32 30 33 39 20 29 35 32 40 41 36 44 Sample Mean 26.75 33.6 38.2 Sample SD 5.38 4.51 4.76 a. Calculate the grand mean, x. b. Calculate the sum of squares between samples, SSE. c. Calculate the sum of squares within samples, SSW. d. Fill in an ANOVA table like the following: Source Sum of Squares df Mean Square F Statistic Between Within Total e. At the 0.01 significance level, conduct a full hypothesis test regarding whether the number of people present seems to influence the time it takes for someone to help someone else in distress. Show all 6 steps. Note that you already calculated the test statistic in parts a. through d. above. You do not need to show additional work for Step 3 of the hypothesis test