Ans_STA3024_Exam1A_Fall2022

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dhne STA 3024 Fall 2022 Exam 1 TEST FORM A STA 3024 Fall 2022 Exam 1 Honor Pledge: “On my honor, | have neither given nor received unauthorized aid on this examination.” SIGN your name in this box in INK Write your UFID number Questions1 -4 Milk chocolate M&M'’s are a small round candy that are multicolored with a chocolate center. They are produced by the Wrigley Confectionary Company, a division of Mars, Inc. It is claimed that the color distribution of all the candies is on average 24% blue, 20% orange, 16% green, 14% yellow, 13% brown and 13% red. You decide to investigate this and take a random sample of 70 M&M'’s from a large bag. The sample color distribution is given in the table below. Color Blue Orange Green Yellow Brown Red Total Observed Count 19 22 15 3 7 4 70 1. Is the variable color categorical or quantitative? Categorical b. Quantitative 2. You are going to perform a Chi-Square Goodness of Fit test. Choose the correct null hypothesis, Hy, for this significance test. a. The company’s given color distribution for milk chocolate M&M’s is independent. b. The company’s given color distribution for milk chocolate M&M'’s is not independent (association). c. The company’s given color distribution for milk chocolate M&M’s is not correct. The company’s given color distribution for milk chocolate M&M'’s is correct. The odds ratio for milk chocolate M&M’s is equal to 1. 3. What is the expected count for thd greenM&M’s? np =10 (C). I(o) = |l & 11.2 b. 15 c. 588 d. 70 e. 1050 4. The assumptions are met. The Chi-Square test statistic is calculated to be x? = 14.21. Using the Chi-Square table, what is the p-value? a. Lessthan0.001 dF; c -1 = CD*,:S Between 0.010 and 0.025 c. Between 0.025 and 0.050 d. Between0.05and 0.1 e. Greater than 0.250

Shine STA 3024 Fall 2022 Exam 1 TEST FORM A Questions 5 -9 NASA’s Artemis | was recently scheduled to launch on September 3, 2022. According to NASA, it will be the first in a series of missions designed to build a long-term human presence at the Moon. Have opinions changed over approximately the last ten years on whether too little is being spent on space exploration? Ina 2012 (group 1) General Social Survey, 203 out of 899 U.S. adults thought that too little was being spent on the space exploration program. In 2021 {group 2), 488 out of 1969 U.S. adults though that too little was being spent. 5. Are these independent or dependent samples? e independent samples b. Dependent samples chfferent qroups (8012, 303.) The assumptions are met. You are going to calculate a 95% confidence interval for the difference in two population proportions. > /P\' _/P\"I =0.2358-02418 A Qb3 0.2258 - - - . . o . - S D| = %qo‘ - 6. What is the value of the|point estimate or this 95% confidence interval’ -0.022 b. 0.0170 c. 02258 =700y (5478 e. 1.96 4% 7~ Po=Heq = 0-a4718 7. The 95% confidence interval is (-0.055, 0.011). Choose the correct interpretation. a. There is a 0.95 probability that the true proportion of U.S. adults who think that too little is being spent on space exploration is between -0.055 and 0.011. b. We are 95% confident that the true proportion of U.S. adults who think that too little is being spent on space exploration is between -0.055 and 0.011. c. We are 95% confident that the sample proportion of U.S adults who think that too little is being spent on the space exploration program in 2012 is between 0.055 less to 0.011 more than in 2021. d. We are 95% confident that the true proportion of U.S adults who think that too little is being spent on the space exploration program in 2012 is between 0.011 less to 0.055 more than in 2021. We are 95% confident that the true proportion of U.S adults who think that too little is being spent on the space exploration program in 2012 is between 0.055 less to 0.011 more than in 2021. A significance test of Hy: p; — p, = O versus H,:p; — p, # 0is carried out. The test statistic is calculated to be z =-1.28, with a p-value = 0.2005. 8. To calculate the test statistic, the pooled proportion p is used. What is the value of the pooled proportion? a. 0.0172 b. 0.0333 /& 0.2258 0 0.2409 e. 0.2478 p= X, tXa _ JOTHURR _ 0. ALL0Y 9. Is the following statement true or false? Mirna B9+ 1969 The 95% confidence interval and the significance test do not agree. This is because 0 is in the confidence interval, so there is no significant evidence of a difference. The p-value of 0.2005 does give significant evidence of a difference. a. True False ’T?\Q;j do g lee P —valie o(_’ 0. 005 does nok \j‘/\/e S&j’uf/gcad duvicden 0,[ 2 dLﬂ&f@nm

Shie STA 3024 Fall 2022 Exam 1 TEST FORM A Questions 10 - 14 Two of the questions asked in the General Social Survey are regarding Job Satisfaction and Happiness. The data is given in the table below. Happiness Job Satisfaction Very Happy Pretty Happy Not too Happy Total Very Satisfied 343 429 71 843 Moderately Satisfied 160 409 87 656 Very Dissatisfied 9 27 28 64 Total 512 865 186 1563 OV 10. For those who reported being ver\‘/)satisfied with their job, what are the percentages for the conditional dstaguton of appiness? Veny heppry Prety Hapey ot too Hapey 17, 9%, 6.4% s e 1 b. 24.4%, 62.3%, 13.3% 3’LHV@‘H> L*"’“‘/?S'-H / K43 ¢ 14.1%,42.2%, 43.8% Lo SO.W/ gq._{,o/o d. 32.8% 55.3%, 11.9% © e. 67.0%, 31.3%, 1.76% You are going to conduct a Chi-Square test for Independence. 11. The assumptions are met. Which of the following are the necessary assumptions for this significance test? I Both groups of data are categorical Data is from a random sample or randomized experiment It Successes and failures in both groups are at least 10 IV. npy=15andn(1 —py) = 15 Expected counts are all at least 5 For credit, you must choose all of the assumptions that apply. a. land!ll only b. 1land IV only I, land V only d. I, Hand IV only e. |, 1land V only 12. What are the degrees of freedom for this significance test? a. 2 4 ¢ 6 d. 9 e. 16 dF: <rﬂ\\)(c~l> = (3-D(3-D -y

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Shine STA 3024 Fall 2022 Exam 1 TEST FORM A 13. If you were to calculate the Chi-Square testjtatlstlc by. and, what is the first term of the calculation? IS X é 0/ o Cxpeched=1a0 x (Yymp b. XZ =276.1+ - . (D x*=162+- X*-e (SLB—a-/m)‘* Fotad Saple Size d x2=13.0+-- Ao - - %q'g)és Jo 2=0.242+ - X =63 e. x + X—“oa&'l---* g 14, Partial Art of Stat output for this test is given below. Pearson's Chi-Squared Test: Test Statistic X2 P-value 112.02 <0.0001 0.0 0 20 40 60 80 100 =112.02 What is the correct conclusion for this significance test? a. With a p-value < 0.0001, there is no significant evidence of an association between job satisfaction and happiness. b. With a p-value < 0.0001, there is significant evidence of independence between job satisfaction and happiness. c. With a p-value < 0.0001, there is no significant evidence that the distribution of happiness given job satisfaction is as claimed. @ With a p-value < 0.0001, there is significant evidence of an association between job satisfaction and happiness.

Shne STA 3024 Fall 2022 Exam 1 TEST FORM A Questions 15 - 19 In a recent Pew Research Center survey of a random sample of 929 Americans aged 18-29, 261 said they have invested in, traded, or used a cryptocurrency. Is there significant evidence that more than 25% of Americans aged 18-29 have used a cryptocurrency? 15. What is the parameter for this significance test? a. P, the true proportion of Americans aged 18-29 who have used a cryptocurrency. b. P, the sample proportion of Americans aged 18-29 who have used a cryptocurrency. p, the true proportion of Americans aged 18-29 who have used a cryptocurrency. d. p, the sample proportion of Americans aged 18-29 who have used a cryptocurrency. e. p; — by, the difference in the true proportion of Americans aged 18-29 who have used a cryptocurrency. 16. The hypothesis for this significance test is Ho:p = 0.25 5 - 0.3809-045_ g g P —(&;C: 0.9%09 Hy:p > 0.25 [Q25(-038) 1 Calculate the test statistic. N 4qaq a. 001 b. 0.25 c. 196 2.18 e. 261 17. The p-value is 0.0147. At what levels of alpha can you reject H,? QREJeCtHOata 0.05 and 0.10 but not at o = 0.01 00T > 0.0l Fa\'[ }D/{j@(//. Ho Reject Hy at a = 0.01 and 0.05 but not at a = 0.10 c. Reject Hy at a = 0.01 but not at a = 0.05 and 0.10 0.0141 £0.0% r@\jeu’ Ho d. Reject H, at all of a = 0.01, 0.05 and 0.10 6.0+ £ 010 (ejec} Ho e. Fail to reject H, at all of a = 0.01, 0.05 and 0.10 ' 18. Given the following two statements: I The necessary assumptions for this significance test are met. v I There is a 0.0147 probability of observing a test statistic as extreme or more extreme than the one observed if the true proportion of Americans aged 18-29 who have used a cryptocurrency is 25%. Which do you agree with? a. lonly b. Il only Both land Il d. Neither of them /@mple p/vpof“(\om L 19. In the question is the value 261/929 = 0.2809 a parameter or @tistic? a. parameter tatistic

Shne STA 3024 Fall 2022 Exam 1 TEST FORM A Questions 20 - 22 The table below gives data for respondents who were asked if it was true that their chances of promotion at their job were good, and about their level of job satisfaction. Job Satisfaction ] Promotion Chances Very Satisfied Very Dissatisfied Total Very True 183 6 189 Not True 111 11 122 Total 294 17 311 20. The relative risk is 1.06. What is the correct interpretation? a. c. d. The odds of being very satisfied with their job in the group who say their promotion chances are very good is 1.06 times the odds of those in the not true group. Respondents who say it is very true that their promotions chances are good are 1.06 times more likely to be very satisfied with their job than those who say it is not true. Respondents who say it is very true that their promotions chances are good are 1.06 times more likely to be very dissatisfied with their job than those who say it is not true. The odds of being very dissatisfied with their job in the group who say their promotion chances are very good is 1.06 times the odds of those in the not true group. 21. Calculate the odds ratio of being very satisfied with their job. a. b. c. e. 0.03 ' P(t=p) p= 183 043 0.9683 35 o = 05 a=Ml _ 6.q08¢ 0.909€% _ 3.03 l0.09 P FE m - 10.09 30.55 = 3.03 22. Which of the following statements are true? a. b. c. Relative risk and the odds ratio are two measures of association. \/ Strong associations will have relative risk far from one. " When one value is the reciprocal of the other, the two values for the odds ratio have the same strength of association. v~ @ All of the above.

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Shine STA 3024 Fall 2022 Exam 1 TEST FORM A Question 23 JMP output is given below from a General Social Survey of a random sample of 20 U.S. adults regarding dog ownership and happiness. Dog: Measured on a scale of 0-1, where 0 = Does not have a dog and 1 = Has a Dog Happy: Measured on a scale of 1-3, where 1 = Very Happy, 2 = Pretty Happy, 3 = Not too Happy 4 = Contingency Table HAPPY Count 1 2 3 Total xpect CellChi*2 0 3 1 6 @ O 1 1587, 20002 09 QXPQQFQOI Counds are less Than 00/14 00(@00@ ’/_"_.,g qf e Six US Total What is the most appropriate significance test that should you carry out with this data? Choose the best option. a. Chi-Square Goodness of Fit test b. Chi-Square test for Independence c. Chi-Square test for Homogeneity @ Fisher’s Exact Test of Independence

Ans_STA3024_Exam1A_Fall2022

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