week 8 Test

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School

American Military University *

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302

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Mathematics

Date

Feb 20, 2024

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docx

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Uploaded by bradymcdede

Attempt Score 19 / 20 - 95 % Overall Grade (Highest Attempt) 19 / 20 - 95 % 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. Hypotheses: H 0 : There is ______ between the general population and the college prep students in GPA. H 1 : 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. no difference, a difference a difference, no difference no difference, no difference a difference, a difference Question 2 1 / 1 point Pamplona, Spain is the home of the festival of San Fermin – The Running of the Bulls. The town is in festival mode for a week and a half every year at the beginning of July. There is a running joke in the city, that Pamplona has a baby boom every April – 9 months after San Fermin. To test this claim, a resident takes a random sample of 300 birthdays from native residents and finds the following observed counts : January 25 February 25 March 27 April 26 May 21

June 26 July 22 August 27 September 21 October 26 November 28 December 26 At the 0.05 level of significance, can it be concluded that births in Pamplona are not equally distributed throughout the 12 months of the year? Enter the p -value - round to 4 decimal places. Make sure you put a 0 in front of the decimal. P-value =___ Answer: 0.9960 Hide question 2 feedback Expected counts will be all the same. 300*(1/12) = 25. The 12 months are either equally distributed or they are not. 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) = 0.9960 n 3 1 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 ___ ___ ___ Expected Counts ___ ___ ___ ___ Answer for blank # 1: 398 (16.67 %)

Answer for blank # 2: 488 (16.67 %) Answer for blank # 3: 714 (16.67 %) Answer for blank # 4: 432 (16.67 %) Answer for blank # 5: 512 (16.67 %) Answer for blank # 6: 656 (16.67 %) Hide question 3 feedback The observed counts are given to you, 398, 488, and 714 Calculate expected counts 1600*.27, 1600*.32 and 1600*.41 n 4 1 A college professor is curious if the location of seat in class affects grades in the class. They are teaching in a lecture hall with 240 students. The lecture hall has 10 rows, so they split the rows into 5 sections – Rows 1-2, Rows 3-4, Rows 5-6, Rows 7-8, and Rows 9-10. At the end of the course, they determine the top 25% of grades in the class, and if the location of the seat makes no difference, they would expect that these top 25% of students would be equally dispersed throughout the classroom. Their observations are recorded below. Run a Goodness of Fit test to determine whether or not location has an impact on the grade. Let α=0.05. Hypotheses: H 0 : Location in the classroom __________ impact final grade. H 1 : Location in the classroom _________ impact final grade. Select the best fit choices that fit in the two blank spaces above. does not, does does, does not does, does does not, does not Question 5 1 / 1 point 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? Enter the expected count for each category in the table below. Round to 1 decimal place. 6 days or less 7-9 days 10-12 days 13 or more days Duration of Sore Throat 49 40 12 9 Expected Counts ___ ___ ___ ___ Answer for blank # 1: 46.2 (25 %) Answer for blank # 2: 34.1 (25 %) Answer for blank # 3: 17.6 (25 %) Answer for blank # 4: 12.1 (25 %) Hide question 5 feedback Expected Counts = 110*.42 110*.31 110*.16 110*.11 n 6 0 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=___ ___ Answer: 0.2005 (0.3913) Hide question 6 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) n 7 1 The manager of a coffee shop wants to know if his customers' drink preferences have changed in the past year. He knows that last year the preferences followed the following proportions – 34% Americano, 21% Cappuccino, 14% Espresso, 11% Latte, 10% Macchiato, 10% Other. In a random sample of 450 customers, he finds that 115 ordered Americanos, 88 ordered Cappuccinos, 69 ordered Espressos, 59 ordered Lattes, 44 ordered Macchiatos, and the rest ordered something in the Other category. Run a Goodness of Fit test to determine whether or not drink preferences have changed at his coffee shop. Use a 0.05 level of significance. Hypotheses: H 0 : There is _______ in drink preference this year. H 1 : There is _______ in drink preference this year. Select the best fit choices that fit in the two blank spaces above. no difference, a difference

a difference, no difference no difference, no difference a difference, a difference Question 8 1 / 1 point A college professor is curious if the location of a seat in class affects grades in the class. They are teaching in a lecture hall with 240 students. The lecture hall has 10 rows, so they split the rows into 5 sections – Rows 1-2, Rows 3-4, Rows 5-6, Rows 7-8, and Rows 9-10. At the end of the course, they determine the top 25% of grades in the class, and if the location of the seat makes no difference, they would expect that these top 25% of students would be equally dispersed throughout the classroom. Their observations are recorded below. Run a Goodness of Fit test to determine whether or not location has an impact on the grade. Let α=0.05. After running a Goodness of Fit test, does the professor have evidence to conclude that location in the classroom has an impact on final grade and what is the p-value? Rows 1-2 Rows 3-4 Rows 5-6 Rows 7-8 Rows 9-10 # in Top 25% 14 8 13 10 15 Expected Counts 12 12 12 12 12 no, the p-value = 0.413907 yes, the p-value = 0.586093 no, the p-value = 0.58609 yes, the p-value = 0.413907 Hide question 8 feedback Use Excel to find the p-value you have the Observed and Expected Counts you can use =CHISQ.TEST( Highlight Observed Counts, Highlight

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