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American Military University *

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Business

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Jan 9, 2024

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docx

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Attempt Score 18 / 20 - 90 % Overall Grade (Highest Attempt) 18 / 20 - 90 % stion 1 1 / 1 p 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. Enter the test statistic - round to 4 decimal places. Test statistic:___ ___ Answer: 7.3315 Hide question 1 feedback 0-0.99 1-1.99 2-2.99 3-4.00 Observed Counts 19 28 82 71 Expected Counts =200*0.07 =14 =200*.21 = 42 =200*.37 = 74 =200*.35 = 70 Test Stat = (19−14)214+(28−42)242+(82−74)274+(71−70)270 Test Stat = 7.331532 n 2 1

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? Enter the p -value - round to 4 decimal places. Make sure you put the 0 in front of the decimal. p -value = ___ ___ Answer: 0.4798 Hide question 2 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 Sagittariu s 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) n 3 1 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 test statistic - round to 4 decimal places. Test statistic =___ ___ Answer: 12.2012 Hide question 3 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

Test Stat = (188−165)2165+(153−137.5)2137.5+(83−99)299+(54−71.5)271.5+(61−66)266+(11−11)211 n 4 1 A company that develops over-the-counter medicines is working on a new product that is meant to shorten the length of sore throats. To test their product for effectiveness, they take a random sample of 110 people and record how long it took for their symptoms to completely disappear. The results are in the table below. The company knows that on average (without medication) it takes a sore throat 6 days or less to heal 42% of the time, 7-9 days 31% of the time, 10-12 days 16% of the time, and 13 days or more 11% of the time. Can it be concluded at the 0.01 level of significance that the patients who took the medicine healed at a different rate than these percentages? After running a Goodness of Fit test, can it be concluded that there is a statistically significant difference in duration of a sore throat for those that took the medicine and what is the p-value? 6 days or less 7-9 days 10-12 days 13 or more days Duration of Sore Throat 49 40 12 9 Expected Counts 46.2 34.1 17.6 12.1 Yes, the p-value = 0.287801 No, the p-value = 0.712199 Yes, the p-value = 0.712199 No, the p-value = 0.287801 Hide question 4 feedback Use Excel to find the p-value you have the Observed and Expected Counts you can use

=CHISQ.TEST( Highlight Observed Counts, Highlight Expected Counts) = 0.287801 0.287801 > .01, Do Not Reject Ho. No, this is not significant. n 5 1 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? Enter the test statistic - round to 2 decimal places. Test statistic=___ ___ Answer: 10.53 Hide question 5 feedback Spring Summer Fall Winter Observed Counts 27 39 31 53 Expected Counts 150*.25 = 37.5 150*.25 = 37.5 150*.25 = 37.5 150*.25= 37.5 Test Stat = (27−37.5)237.5+(39−37.5)237.5+(31−37.5)237.5+(53−37.5)237.5 n 6 1 A color code personality test categorizes people into four colors – Red (Power), Blue (Intimacy), Green (Peace), and Yellow (Fun). In general, 25% of people are Red, 35% Blue, 20% Green, and 20% Yellow. An art class of 45 students is tested at a university and 7 are found to be Red, 18 Blue, 9 Green, and 11 Yellow. Can it be concluded that personality type has an impact on students' areas of interest and talents, such as artistic

students and state the p-value? Test at a 0.05 level of significance. Red Blue Green Yellow Observed Counts 7 18 9 11 Expected Counts 11.25 15.75 9 9 Yes, the p-value = 0.501025 No, the p-value = 0.501025 No, the p-value = 0.498975 Yes, the p-value = 0.498975 Hide question 6 feedback Use Excel to find the p-value you have the Observed and Expected Counts you can use =CHISQ.TEST( Highlight Observed Counts, Highlight Expected Counts) = 0.498975 0.498975 > .05, Do Not Reject Ho. No, this is not significant. Use Excel to find the p-value you have the Observed and Expected Counts you can use =CHISQ.TEST( Highlight Observed Counts, Highlight Expected Counts) = 0.498975 0.498975 > .05, Do Not Reject Ho. No, this is not significant. n 7 1 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

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