STA 3024 Exam 3 Practice ProblemsNOTE: These are just Practice Problems. This is NOT meant to look just like the test,and it is NOT the only thing that you should study. Make sure you know all the material from the notes, quizzes, suggested homework and the corresponding chapters in the book.Questions 1 – 7 Former kicker for the Gator football team, Chris Hetland, was very good atmaking field goals in the 2005 season, but in the 2006 regular season had only made 3 out of 12. The following is the Logistic Regression Output to predict the probability of making a field goal (yes/no), based on how far the kick is (in yards) and the year (2005 or 2006).Logistic Regression Table Predictor Coef SE Coef Z P Constant 8312.97 3073.50 2.70 0.007yards -0.173760 0.0901421 -1.93 0.054 year -4.14174 1.53141 -2.70 0.007 1. What kind of variables do we have here?a) a quantitative predictor and a quantitative responseb) two quantitative predictors and a quantitative responsec) a quantitative predictor and a categorical responsed) two quantitative predictors and a categorical response2. Write down the fitted logistic regression equation:a) yˆ= 8312.97 – 0.173760 – 4.14174b) yˆ= 8312.97 – 0.173760 yards – 4.14174 yearc) pˆ= e 8312.97 – 0.173760 – 4.14174 / 1+ e 8312.97 – 0.173760 – 4.14174d) pˆ= e 8312.97 – 0.173760 yards – 4.14174 year / 1+ e 8312.97 – 0.173760 yards – 4.14174 year3. The coefficients of yards and years are both negative. This means:a) that neither variable is a good predictor of whether the kicker will make or not the field goalb) that simple linear regression would have been more appropriate than logistic regressionc) that there was a mistake in the way the data was entered into the computerd) that the chances of making the field goal go down as the yardage increases, and as the years increaseFind the probability of making a field goal:4. from the 30 yd line in 20065. from the 30 yd line in 20056. from the 40 yd line in 20067. from the 40 yd line in 2005Question 8 - 13 As part of a project for their Intro Stat course, two students compared twobrands of chips, Frito Lays and Golden Flakes, to see which company gives you more for your money. Five bags of each brand (which, according to the label, each contained 35.4 grams) were measured with a very accurate scale. Use the Wilcoxon Rank-Sum test to see ifthere are any significant differences between the two brands in the amount of product they put in their bags.Frito Lays: 35.3 35.4 35.8 35.9 35.9 Golden Flake: 35.3 37.8 38.8 38.1 42.5 8. The null hypothesis is about:a) the mean contents of the bags for Frito Lays and Golden Flakes brandsb) the mode of the contents of the bags for Frito Lays and Golden Flakes brandsc) the distribution of the contents of the bags for the two brandsd) the number of bags with contents below the label weight for the two brands9. The alternative hypothesis, according to the problem stated above, is that:a) Frito Lays gives you more chips than Golden Flakesb) Frito Lays gives you less chips than Golden Flakesc) Frito Lays gives you either more or less chips than Golden Flakesd) Golden Flakes gives you more chips than the amount stated on the label10. The bags that contained 35.9 grams will receive a rank of:a) 4 b) 4.5c) 5 d) 5.5 e) 611. The p-value for the test was .1164. We conclude that:a) Frito Lays gives you more chips.b) Golden Flakes gives you more chips.c) There is not enough evidence to prove a difference between the two brands.d) There is enough evidence to prove a difference between the two brands.12. If the assumptions for the Normal based procedure were satisfied, we could analyze the data with a confidence interval for:a) μ b) μ1-μ2c) μdd) η1- η 213. Why is it not a good idea to use the Normal-based procedure here?a) the data was not randomly selectedb) the data does not have a continuous distributionc) the outlier violates the assumption of Normalityd) the nonparametric method is always betterQuestions 14 - 18 Do plain and peanut m&m's have the same distribution of colors?Several bags of each variety (plain and peanut) were randomly selected, and the number of candies of each color were counted before eating any of them. The data appears below.brown yellow red blue green orangeplain 81 84 41 17 30 41 294peanut 17 7 27 13 14 16 9498 91 68 30 44 57 38814. The null hypothesis is that:a) plain and peanut varieties are independentb) the colors are independent of each otherc) color and variety are independent of each otherd) all of the above15. The expected number of blue, peanut m&m's (under independence) is:a) 15.0 b) 15.67c) 7.27 d) 32.3316. The sampling distribution is χ2 with degrees of freedom equal to:a) 5 b) 10 c) 11 d) 1217. The test statistic was 32.67. Use the table to approximate the p-value for this test:a) smaller than .001b) equal to .05c) between .05 and .10d) between .950 and .97518. What conclusions can you reach from this analysis, based on the data and the test statistic given?a) There is something wrong with the data, maybe the m&m's were not randomly selected.b) The distribution of colors is not significantly different for plain and peanut m&m's.c) Peanut m&m's are significantly more colorful than plain m&m's.d) There are significantly more brown m&m's than orange m&m's.Questions 19 - 21 Match each of the Nonparametric procedures presented on the left withthe corresponding experimental design from the list on the right (use each alternative only once).19. Kruskal-Wallis H Test a) two independent samples20. Wilcoxon Rank-Sum Test b) paired samples21. Wilcoxon Signed-Rank Test c) several independent samplesQuestions 22 -24 Five sets of identical twins were selected at random from a population ofidentical twins. One child was selected at random from each pair to form an "experimental group." These five children were sent to school. The other five children were kept at home as a control group. At the end of the school year the following IQ scores were obtained. Does this evidence justify the conclusion that lack of school experience has a depressing effect on IQ scores? Analyze the data with the Wilcoxon Signed-Rank TestExperimental ControlPair Group Group 1 110 112 2 125 120 3 139 128 4 142 135 5