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Fall 2023 STAT 240 Final Exam i | A Acpr wal - _Va'bhaw . 105818069 1st Letter of Last/Family Name Last/ Family Name as in Canvas First /Given Name as in Canva.s Student ID Instructor (Circle) Bret Larget : / Bi Cheng \Xfu\ Lecture (Circle). MWF 8:50-9:40 MWF 9:55-10:45 WF 2:25-3:15 MWF 3:30-4:20 Instructions: 1. You may use both sides of two regular sheet of paper Wlth self- prepared notes. 2 You may not consult other resources, your phone a computer, online mfo nor your neighbor’s exam. : 3. Do all of your Work in the space provided. Use the backs of pages if necessary, indicating clearly that you have done so (so the grader can easily find your complete answer). Scoring Question | Name/Course | 1-3 [ 4-8 [ 912 | 13 [ 14] 15 | 16 | Total Points ey - 0. bW w2 ol T S (L Possible |2 12 720 |16 [12]13 117141007
Multiple Choice and Short Answer. (4 points each) For each multiple choice problem, circle the letter for all correct answers and cross out the‘ letter for all incorrect answers. Answer briefly for other problems. j Problem 1. Sketch the density plot of a normal distribution, 1nclud1ng labeling the z axis, where the mean and median are 100 and the standard deviation is about 20, using a dotted or dashed line. (// Over this, sketch another density plot using a solid line with the same median and about.the same . - ‘standard deviation, but with a slight/moderate right skewness. B g diras i ) W» oo /»«F?’D Problem 2. A data set bm has Boston Marathon data from the year 2010 with a row for each runner who completed the race and variables Age, Age Range, and Time. Identify code that calculates the mean time for all runners between the ages of 35 and 39. Note: Age_ Range equals “35-39” when Age is in this range and code which calculates the desired mean along with other things should be circled as correct. Circle correct answers and cross out incorrect answers. @ bm %>% filter(Age_Range == "35-39") %>Y summarize (mean = mean (Time) ) 2 (\b{f bm %>Y% group_by(Age_Range) %>}, summarize (mean = mean(Time)) (©) bm %>% mutate(mean = mean(Time)) %>% filter(between(Age, 35, 39)) ‘gfifj bm %>% select(Age Range == "35-39") %>% summarize(mean = mean (Time)) Problem 3. The probablllty mass function of a discrete random varlable X is plotted here. It has L/ a mean u and a standard dev1at10n . 0.3 0.2 I X . @ 0.1- I 0.0 — : ; , 10 20 | 30 : 40 50 : X Write the following four numbers under their corresponding valfieé: 12.7;.33; 40, 70 | Wy o 08 quantile 100 x P(X > 20) FX S | S o . 70
Pnoblems 4 and 5. | h ” ’Eb A data frame matches contains 4746 rows, one for each match between two teams, with the variables index, W, and L, where index is the row number and W and L have the names of one of 332 teams that won and lost a match, respectlvely Each of the 332 teams appears at least once in columns W and L. The data frame ncaa has 64 rows and columns Team and Conference where each value “in Team is distinct and is one of the same 332 team names in matches. Conference is another & ) & categomcal variable with 32 distinct values. : Vo, W L The data frame df is created by the following code. ’ i - df = matches %>% . A _ a7 pivot_longer(W:L, names_to = "Result", values to = "Team") %>% ‘ count (Team, Result) %>% ¥ - . e pivot_wider(names_from = Result, values_from = n) %>% I - semi_join(ncaa, by = "Team") o ' s Problem 4. How 'manyyrows are in df? - W1 [Ms2 ©6s /@H;T:asz . (8 4746 Problem 5. List the column names (in any order) in df. Teari, W, L, conlerence Problem 6. A random variéble X is created by adding together the number of heads in five tosses of a fair coin plus the number of tails in a different set of five tosses of the same coin. Circle correct answers and cross out incorrect answers. @ X has a binomial distribution X is not binomial because the number of trials is not fixed - . X is not binomial because the trial success probability changes (@) X is not binomial because the trials are not independent. Problem 7. When constructing a 95% confidence interval for a single population proportion from sample of size n = 105, the margin of error is some quantity a times an estimated standard - error. How is the value of ¢ determined? Circle all correct answers and cross out 1nc0rrect } answers bl anorn(0.95) (@) quorm(0.975) () qt(0.975, 104) (M qt(0.975, 103) Problem 8 In the test of a hypoth651s test for a population proportion p with Hp : p = 0.5 versus H, : p > 0.5, the p-value is equal to 0 043. Circle correct answers and cross out incorrect answers. : We have proven that p > 0.5. The probability that p > 0.5 is more than 95%. : g There is evidence that p > 0.5. : If we had tested with the two-sided alternative hypothesis, the test would have been statistically significant at the o = 0.05 level.
Problem 9. Put the following four quantities in order from smallest to largest. (a) qnorm(0. 1) (b) gti(0.1,:5) fe) g0 L, 10) (d) gt (0.1, 100) jronlon) < ghlo-l 00 < ghlorl, 10) < gHlofi t ~ Problem 10. The correlation coefficient between the avérage height in inches (plotted on the x axis) and weight in pounds (plotted on the y axis) of a sample of 100 people is r = 0 68. Clrcle correct answers and cross out incorrect answers. . (6) If height were measured in feet instead of inches, the value of r would be r = 0.68/12. / ‘.Q In this sample, relatively tall people tend to weigh more than relatlvely short people do. : @" 68% of the points fall exactly on a straight line. ' j L If we switched the axes, the new correlation coefficient Would be equal to —0 68. Problem 11. A linear regression model predicts Welght from he1ght from a sample of 100 people with a mean height of 67 inches. The correlation coefficient is r = 0.68. How much heavier than - average is the predicted weight of a person who is 73 inches tall if the standard deviation of heights- in the data is 4 inches and the standard deviation of weights is 30 pounds? (Note that 78 1is 6 inches above the mean height of 67 inches.) Do not simplify your answer. /&{L/ be weipht L 5 be haight \/,,}7: ZY’} Iuhu(, Zfi'g;..}-(, : . / S 2 \/ y M) f‘Sy ‘ - ' :" ' : ’;<w\\(05?)(}a/ T\/ . @uz}f” gy ] Problem 12a. Usmg the same settlng as the previous problem Which of the follovvlng 1ntervals is the Wldest7 Circle the correct answer and cross out the 1ncorrect answers. A 95% confidence. interval for the mean weight of all people who are 65 inches tall. % A 95% confidence interval for the mean weight of all people who are 73 inches tall. / A 95% prediction interval for the weight of a single individual who is 65 inches tall. @ A 95% prediction 1nterva1 for the weight of a smgle individual who is 73 inches tall. Problem 12b. 'Using the same setting as the previous problem: Which of the following intervals 1s ~ the narrowest? Circle the correct answer and cross out the incorrect answers. / @ A confidence interval for the mean Weight- of all people who are 65 inches tall. A confidence interval for the mean weight of all people who are 73 inches tall. 4@@) A prediction interval for the weight of a single individual who is 65 inches tall. ;fi) A prediction interval for the weight of a smgle 1nd1v1dual who is 73 inches tall.
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