MAT 302 WEEK 8 TEST 2

Week 8 Test Return to Assessment List Part 1 of 4 - Chi Square Test for Homogeneity 8.0/ 8.0 Points Question 1 of 20 1.0/ 1.0 Points A company manager believes that a person’s ability to be a leader is directly correlated to their zodiac sign. He never selects someone to chair a committee without first evaluating their zodiac sign. An irate employee sets out to prove her manager wrong. She claims that if zodiac sign truly makes a difference in leadership, then a random sample of 210 CEO’s in our country would reveal a difference in zodiac sign distribution. She finds the following zodiac signs for her random sample of 210 CEO’s: Births Signs 25 Aries 13 Taurus 17 Gemini 21 Cancer 16 Leo 18 Virgo 15 Libra 16 Scorpio 20 Sagittarius 11 Capricorn 23 Aquarius 15 Pisces Can she conclude that zodiac sign makes a difference in whether or not a person makes a good leader? Alpha = .10. • A. yes because the p-value = 0.5523 • B. no because the p-value = 0.5523 • C. yes because the p-value = 0.4798 • D. no because the p-value = 0.4798 Answer Key:D Feedback: The Expected Count is all the same value. 210*(1/12) = 17.5 Births Signs Expected Count 25 Aries 17.5 13 Taurus 17.5 17 Gemini 17.5 21 Cancer 17.5 16 Leo 17.5 18 Virgo 17.5 15 Libra 17.5 16 Scorpio 17.5 20 Sagittarius 17.5 11 Capricorn 17.5 23 Aquarius 17.5 15 Pisces 17.5 Use Excel to find the p-value =CHISQ.TEST(Highlight Observed, Highlight Expected) p-value .05, Do Not Reject Ho. No this is not significant. Question 2 of 20 1.0/ 1.0 Points Click to see additional instructions Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale – with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1’s, 15% 2’s, 34% 3’s, and 41% 4’s. Mr. Goodman sets a goal to outscore these numbers. At the end of the year he takes a random sample of his evaluations and finds 10 1’s, 13 2’s, 48 3’s, and 52 4’s. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Department’s? Enter the p-value - round to 4 decimal places. Make sure you put a 0 in front of the decimal. p-value= 0.3913 Answer Key:0.3913 Feedback: 1's 2's 3's 4's Observed Counts 10 13 48 52 Expected Counts 123 *.10 = 12.3 123*.15 = 18.45 123*.34 = 41.82 123*.41 = 50.43 Use Excel to find the p-value =CHISQ.TEST(Highlight Observed, Highlight Expected) Question 3 of 20 1.0/ 1.0 Points Click to see additional instructions A large department store is curious about what sections of the store make the most sales. The manager has data from ten years prior that show 30% of sales come from Clothing, 25% Home Appliances, 18% Housewares, 13% Cosmetics, 12% Jewelry, and 2% Other. In a random sample of 550 current sales, 188 came from Clothing, 153 Home Appliances, 83 Housewares, 54 Cosmetics, 61 Jewelry, and 11 Other. At α=0.10, can the manager conclude that the distribution of sales among the departments has changed? Enter the p-value - round to 4 decimal places. Make sure you put a 0 in front of the decimal. p-value= 0.0321 Answer Key:0.0321 Feedback: Clothing Home App. Housewares Cosmetics Jewelry Other Observed Counts 188 153 83 54 61 11 Expected Counts 550*.30 = 165 550*.25 = 137.5 550*.18 = 99 550*.13 = 71.5 550*.12 = 66 550*.02= 11 Use Excel to find the p-value =CHISQ.TEST(Highlight Observed, Highlight Expected) Question 4 of 20 1.0/ 1.0 Points Click to see additional instructions The permanent residence of adults aged 18-25 in the U.S. was examined in a survey from the year 2000. The survey revealed that 27% of these adults lived alone, 32% lived with a roommate(s), and 41% lived with their parents/guardians. In 2008, during an economic recession in the country, another such survey of 1600 people revealed that 398 lived alone, 488 lived with a roommate(s), and 714 lived with their parents. Is there a significant difference in where young adults lived in 2000 versus 2008? Test with a Goodness of Fit test at α=0.05. Enter the observed and expected counts for each category in the table below. Round to whole numbers. Alone Roommates Parents/Guardians Observed Counts 398 488 714 Expected Counts 432 512 656 Answer Key:398, 488, 714, 432, 512, 656 Feedback: The observed counts are given to you, 398, 488, and 714 Calculate expected counts 1600*.27, 1600*.32 and 1600*.41 Question 5 of 20 1.0/ 1.0 Points An urban economist is curious if the distribution in where Oregon residents live is different today than it was in 1990. She observes that today there are approximately 3,109 thousand residents in NW Oregon, 902 thousand residents in SW Oregon, 244 thousand in Central Oregon, and 102 thousand in Eastern Oregon. She knows that in 1990 the breakdown was as follows: 72.7% NW Oregon, 20.7% SW Oregon, 4.8% Central Oregon, and 2.8% Eastern Oregon. Can she conclude that the distribution in residence is different today at a 0.05 level of significance? Hypotheses: H0: There is ________ in the distribution of Oregon residents today. H1: There is ________ in the distribution of Oregon residents today. • A. no difference, a difference • B. a difference, no difference • C. no difference, no difference • D. a difference, a difference Answer Key:A Question 6 of 20 1.0/ 1.0 Points A college prep school advertises that their students are more prepared to succeed in college than other schools. To verify this, they categorize GPA’s into 4 groups and look up the proportion of students at a state college in each category. They find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in GPA. They then take a random sample of 200 of their graduates at the state college and find that 19 has a 0-0.99, 28 have a 1-1.99, 82 have a 2-2.99, and 71 have a 3-4.00. Can they conclude that the grades of their graduates are distributed differently than the general population at the school? Test at the 0.05 level of significance. Hypotheses: H0: There is ______ between the general population and the college prep students in GPA. H1: There is ______ between the general population and the college prep students in GPA. Select the best fit choices that fit in the two blank spaces above. • A. no difference, a difference • B. a difference, no difference • C. no difference, no difference • D. a difference, a difference Answer Key:A Question 7 of 20 1.0/ 1.0 Points A Driver’s Ed program is curious if the time of year has an impact on number of car accidents in the U.S. They assume that weather may have a significant impact on the ability of drivers to control their vehicles. They take a random sample of 150 car accidents and record the season each occurred in. They found that 27 occurred in the Spring, 39 in the Summer, 31 in the Fall, and 53 in the Winter. Can it be concluded at the 0.05 level of significance that car accidents are not equally distributed throughout the year? Hypotheses: H0: Car accidents ________ equally distributed throughout the year. H1: Car accidents ________ equally distributed throughout the year. Select the best fit choices that fit in the two blank spaces above. • A. are, are not • B. are not, are • C. are, are • D. are not, are not Answer Key:A Question 8 of 20 1.0/ 1.0 Points Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale – with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1’s, 15% 2’s, 34% 3’s, and 41% 4’s. Mr. Goodman sets a goal to outscore these numbers. At the end of the year he takes a random sample of his evaluations and finds 10 1’s, 13 2’s, 48 3’s, and 52 4’s. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Department’s? Hypotheses: H0: There is _________ in Mr. Goodman’s evaluations and the History Department’s. H1: There is _________ in Mr. Goodman’s evaluations and the History Department’s. Select the best fit choices that fit in the two blank spaces above. • A. no difference, a difference • B. a difference, no difference • C. no difference, no difference • D. a difference, a difference Answer Key:A