The U.S. Department of Agriculture (USDA) Center for Nutrition Policy and Promotion (CNPP) uses the Healthy Eating Index to monitor the diet quality of the U.S. population, particularly how well it conforms to dietary guidance. The HEI–2005 measures how well the population follows the recommendations of the 2005 Dietary Guidelines for Americans (Guenther et al. 2007). Data collected on a random sample of individuals who participated in two extended interviews and medical examinations are contained in the data file HEI Cost Data Variable Subset, where the first interview is identified by daycode = 1 and data for the second interview are identified by daycode = 2. One variable in the HEI–2005 study is a participant’s activity level, coded as 1 = sedentary, 2 = active, and 3 = very active. Previously, we constructed bar charts of participants’ activity level by gender for data collected on the first interview. Determine if there is an association between activity level and gender.

$$\begin{array}{lcc} \hline \text { Activity Level } & \text { Male } & \text { Female } \\ \hline \text { Sedentary } & 957 & 1226 \\ \text { Active } & 340 & 417 \\ \text { Very active } & 842 & 678 \\ \hline \end{array}$$

A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population distribution of amounts spent is normal.

In a period of 100 minutes there were a total of 190 arrivals at a highway toll booth. The accompanying table shows the frequency of arrivals per minute over this period. Test the null hypothesis that the population distribution is Poisson.

$$\begin{array}{lccccc} \hline \text { Number of arrivals } & & & & & \\ \text { in minutes } & 0 & 1 & 2 & 3 & 4 \text { or more } \\ \hline \text { Observed frequency } & 10 & 26 & 35 & 24 & 5 \\ \hline \end{array}$$

The number of times a machine broke down each week was observed over a period of 100 weeks and recorded in the accompanying table. It was found that the average number of breakdowns per week over this period was 2.1. Test the null hypothesis that the population distribution of breakdown is Poisson.

$$\begin{array}{lcccccc} \hline \text { Number of breakdowns } & 0 & 1 & 2 & 3 & 4 & 5 \text { or more } \\ \hline \text { Number of weeks } & 10 & 24 & 32 & 23 & 6 & 5 \\ \hline \end{array}$$

A random sample of statistics professors was asked to complete a survey including questions on curriculum content, computer integration, and software preferences. Of the 250 responses, 100 professors indicated that they preferred software package M and 80 preferred software package E, whereas the remainder were evenly split between preference for software package S and software package P. Do the data indicate that professors have a preference for any of these software packages?

A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly distributed over the three stations.

$$\begin{array}{lccc} \hline \text { Station } & \text { A } & \text { B } & \text { C } \\ \hline \text { Number of first preferences } & 47 & 42 & 61 \\ \hline \end{array}$$

At a certain school 60 of the 100 boys and 60 of the 80 girls signed up for the senior trip. Is there an association between going on the trip and gender identity? A) We can't tell, because the class doesn't have the same number of boys and girls. B) Yes, because the same number of boys and girls signed up. C) Yes, because a lower percentage of boys signed up than of girls. D) No, because the people on the trip were 50% boys and 50% girls.

A systolic blood pressure of 120 would be considered normal. One of 150 would be high. But since blood pressure varies with gender and increases with age, a better gauge of the relative standing of your blood pressure would be obtained by comparing it with the population of blood pressures of all persons of your gender and age in the United States. Of course, we can not supply you with that data set, but we can show you a very large sample selected from it. The blood pressure data on 1910 persons, 965 men and 945 women between the ages of 15 and 20, are found at the CourseMate Web site. The data are part of a health survey conducted by the National Institutes of Health (NIH). Entries for each person include that person's age and systolic and diastolic blood pressures at the time the blood pressure was recorded.

Consider the 965 men and 945 women as the entire population of interest. Choose a sample of n=50 men and n=50 women, recording their systolic blood pressures and their ages. Draw two relative frequency histograms to graphically display the systolic blood pressures for your two samples. Do the shapes of the histogram resemble the population histograms from part 3?

For $12$ recent clients, a weight-loss clinic has collected the following data. (Session is coded as 1 for day, 0 for evening. Gender is coded as 1 for male, 0 for female.) Using a computer statistical package, carry out a multiple regression analysis, interpret the partial regression coefficients, and discuss the results of each significance test.

$$\begin{array}{ccccc} \text { Client } & \begin{array}{c} \text { Pounds } \\ \text { Lost } \end{array} & \begin{array}{c} \text { Months as } \\ \text { a Client } \end{array} & \text { Session } & \text { Gender } \\ \hline 1 & 31 & 5 & 1 & 1 \\ 2 & 49 & 8 & 1 & 1 \\ 3 & 12 & 3 & 1 & 0 \\ 4 & 26 & 9 & 0 & 0 \\ 5 & 34 & 8 & 0 & 1 \\ 6 & 11 & 2 & 0 & 0 \\ 7 & 4 & 1 & 0 & 1 \\ 8 & 27 & 8 & 0 & 1 \\ 9 & 12 & 6 & 1 & 1 \\ 10 & 28 & 9 & 1 & 0 \\ 11 & 41 & 6 & 0 & 0 \\ 12 & 16 & 6 & 0 & 0 \end{array}$$

Undergraduate students at Miami University in Oxford, Ohio, were surveyed in order to evaluate the effect of price on the purchase of a pizza from Pizza Hut. The students were asked to suppose that they were going to have a large two-topping pizza delivered to their residence. Then they were asked to select from either Pizza Hut or another pizzeria of their choice. The price they would have to pay to get a Pizza Hut pizza differed from survey to survey. For example, some surveys used the price $11.49 . Other prices investigated were$ 8.49, $9.49,$ 10.49, $12.49,$ 13.49 , and $ 14.49 . The dependent variable for this study is whether or not a student will select Pizza Hut. The independent variables are the price of a Pizza Hut pizza and the gender of the student (1= male, 0= female ) . The results of these surveys are stored in PizzaHut .

a. Using half the data as the training sample and the other half of the data as the validation sample, develop a classification tree model to predict the probability the student will select Pizza Hut based on the price of a Pizza Hut pizza and the gender of the student.

b. What conclusions can you reach about the probability the student will select Pizza Hut?

Repeat step 1 for variables 27 and 17. Can we conclude that the education level of the respondent is independent of the shopping area judged best for bargains?

1,2 , and 3 = Frequency of shopping at Springdale Mall, Downtown, and West Mall, respectively 4,5 , and $6=$ Typical amount spent during a trip to Springdale Mall, Downtown, and West Mall, respectively $17=$ The area identified as best for bargain sales $26=$ Gender of the respondent $27=$ Education level of the respondent $28=$ Marital status of the respondent

An experiment involving a gender-selection method includes a control group of 15 couples who are not given any treatment intended to influence the genders of their babies. Each of the 15 couples has one child. a. Construct a table listing the possible values of the random variable x (which represents the number of girls among the 15 births) and the corresponding probabilities. b. Find the mean and standard deviation for the numbers of girls in such groups of 15. c. If the couples have 10 girls and 5 boys, is that result unusual? Why or why not?

Compare and contrast the female characters in the play — Cecily and Gwendolen with Lady Bracknell and Miss Prism. What is Wilde’s attitude toward women in this play? Compare and contrast that attitude with his attitude toward Algernon and Jack. Does Wilde seem to have more sympathy for the women or for the men? Is one gender portrayed as more foolish, more clever, more self-aware, more naive? When devising your answer, consider the different schemes with which male and female characters deceive others and themselves throughout the play.

In a study of the lung function of children, the volume of air exhaled under force in one second is called $\mathrm{FEV}_{1}.$ $(FEV_{1}$ stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year’s $\mathrm{FEV}_{1}$ as a function of last year’s $\mathrm{FEV}_{1}$ (in liters), the child’s gender (0 = Male, 1 = Female), the child’s height (in m), and the ambient atmospheric pressure (in mm). The following MINITAB output presents the results of fitting the model $\mathrm{FEV}_{1}=\beta_{0}+\beta_{1} \text { Last } \mathrm{FEV}_{1}+\beta_{2} \text { Gender }+\beta_{3} \text { Height }+\beta_{4} \text { Pressure }+\varepsilon$ $$ \begin{matrix} \text{The regression equation is}\\ \text{FEV1 = −0.219 + 0.779 Last FEV − 0.108 Gender + 1.354 Height − 0.00134 Pressure}\\ \text{Predictor} & \text{Coef} & \text{SE Coef} & \text{T} & \text{P}\\ \text{Constant} & \text{−0.21947} & \text{0.4503} & \text{−0.49} & \text{0.627}\\ \text{Last FEV} & \text{0.779} & \text{0.04909} & \text{15.87} & \text{0.000}\\ \text{Gender} & \text{−0.10827} & \text{0.0352} & \text{−3.08} & \text{0.002}\\ \text{Height} & \text{1.3536} & \text{0.2880} & \text{4.70} & \text{0.000}\\ \text{Pressure} & \text{−0.0013431} & \text{0.0004722} & \text{−2.84} & \text{0.005}\\ \text{S = 0.22039} & \text{R-Sq = 93.5\\%} & \text{R-Sq(adj) = 93.3\\%}\\ \text{Analysis of Variance}\\ \text{Source} & \text{DF} & \text{SS} & \text{MS} & \text{F} & \text{P}\\ \text{Regression} & \text{4} & \text{111.31} & \text{27.826} & \text{572.89} & \text{0.000}\\ \text{Residual Error} & \text{160} & \text{7.7716} & \text{0.048572}\\ \text{Total} & \text{164} & \text{119.08}\\ \end{matrix} $$ a. Predict the $\mathrm{FEV}_{1}$ for a boy who is 1.4 m tall, if the measurement was taken at a pressure of 730 mm and last year’s measurement was 2.113 L. b. If two girls differ in height by 5 cm, by how much would you expect their $FEV_1$ measurements to differ, other things being equal? c. The constant term $\beta_{0}$ estimated to be negative. But $FEV_1$ must always be positive. Is something wrong? Explain.