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Obstacle Course Times An obstacle course was set up on a campus, and 12 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at a= 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. 1 2 3 4 5 6 7 8 9 10 11 12 Student Before 81 77 67 75 72 80 70 78 82 69 68 76 After 76 73 68 68 70 76 65 75 78 65 70 73 Send data to Excel Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Họ: (Choose one) H: (Choose one) This hypothesis test is a (Choose one) test.

Obstacle Course Times An obstacle course was set up on a campus, and 12 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at a= 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. 1 2 3 4 5 6 7 8 9 10 11 12 Student Before 81 77 67 75 72 80 70 78 82 69 68 76 After 76 73 68 68 70 76 65 75 78 65 70 73 Send data to Excel Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Họ: (Choose one) H: (Choose one) This hypothesis test is a (Choose one) test.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A ALEKS - Google Chrome A www-awu.connectmath.com/alekscgi/x/Isl.exe/1cqJCkxOUkfU30pEIASLkB2_hW4nmFZxw4EDq4u2zFQT1HSdvxh.. Q Sample Question Obstacle Course Times An obstacle course was set up on a campus, and 11 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at a = 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. Student 1 3 4 8 9 10 11 Before 70 78 82 75 69 68 76 81 77 67 72 After 65 75 78 68 65 70 73 76 73 68 70 Send data to Excel (a) State the hypotheses and identify the claim. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim. The null hypothesis H, is the statement that the difference between the matched pairs is zero. This is equivalent to un = 0. The alternative hypothesis H, is the statement that there is a difference between the matched pairs. Since we are interested to see if the students did better the second time (time before must be greater than time after), the differences must be greater than zero. This is equivalent to un >0. The problem asks if "the students did better the second time." Hence, the claim is the alternative hypothesis H,. (b) Find the critical value(s). For n= 11, the degrees of freedom are d.f. = 11-1=10. From OThe t Distribution Table, for a right-tailed test with a = 0.05 and d.f. = 10, the critical value is 1.812. (c) Compute the test value. First, make a table to find the differences of the values of the pairs of data, D, the square of the differences, D', and find the totals of D (E D) and D(E D²). Before (X) After (X2) Next, find the mean of the differences. D. snd the standard D=X-X, devistion of the differences. Sn 70 65 5 25 D = 78 75 3 9 34 82 78 4 16 - 3.091 75 68 7 49 nE D- (E D n (n-1) 69 65 4 16 68 70 -2 4 11(174) - (34) 11 (11 - 1) 76 73 3 81 76 5 25 758 V 110 - 2.625 77 73 4 16 67 68 -1 1 Using the formula for the : test-for testing the difference between two means-dependent samples, compute the test valuer 72 70 2 4 Σ D= 34 ED = 174 Next, find the mean of the differences, D. and the standard deviation of the differences, Sn: 3.091 -0 2.625//11 ED D = - 3.905 Hence, the test value rounded to three decimal places is -3.905 34
Transcribed Image Text:A ALEKS - Google Chrome A www-awu.connectmath.com/alekscgi/x/Isl.exe/1cqJCkxOUkfU30pEIASLkB2_hW4nmFZxw4EDq4u2zFQT1HSdvxh.. Q Sample Question Obstacle Course Times An obstacle course was set up on a campus, and 11 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at a = 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. Student 1 3 4 8 9 10 11 Before 70 78 82 75 69 68 76 81 77 67 72 After 65 75 78 68 65 70 73 76 73 68 70 Send data to Excel (a) State the hypotheses and identify the claim. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim. The null hypothesis H, is the statement that the difference between the matched pairs is zero. This is equivalent to un = 0. The alternative hypothesis H, is the statement that there is a difference between the matched pairs. Since we are interested to see if the students did better the second time (time before must be greater than time after), the differences must be greater than zero. This is equivalent to un >0. The problem asks if "the students did better the second time." Hence, the claim is the alternative hypothesis H,. (b) Find the critical value(s). For n= 11, the degrees of freedom are d.f. = 11-1=10. From OThe t Distribution Table, for a right-tailed test with a = 0.05 and d.f. = 10, the critical value is 1.812. (c) Compute the test value. First, make a table to find the differences of the values of the pairs of data, D, the square of the differences, D', and find the totals of D (E D) and D(E D²). Before (X) After (X2) Next, find the mean of the differences. D. snd the standard D=X-X, devistion of the differences. Sn 70 65 5 25 D = 78 75 3 9 34 82 78 4 16 - 3.091 75 68 7 49 nE D- (E D n (n-1) 69 65 4 16 68 70 -2 4 11(174) - (34) 11 (11 - 1) 76 73 3 81 76 5 25 758 V 110 - 2.625 77 73 4 16 67 68 -1 1 Using the formula for the : test-for testing the difference between two means-dependent samples, compute the test valuer 72 70 2 4 Σ D= 34 ED = 174 Next, find the mean of the differences, D. and the standard deviation of the differences, Sn: 3.091 -0 2.625//11 ED D = - 3.905 Hence, the test value rounded to three decimal places is -3.905 34
Obstacle Course Times An obstacle course was set up on a campus, and 12 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at a= 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. 1 2 3 4 5 6 7 8 9 10 11 12 Student Before 81 77 67 75 72 80 70 78 82 69 68 76 After 76 73 68 68 70 76 65 75 78 65 70 73 Send data to Excel Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Họ: (Choose one) H: (Choose one) This hypothesis test is a (Choose one) test.
Transcribed Image Text:Obstacle Course Times An obstacle course was set up on a campus, and 12 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at a= 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. 1 2 3 4 5 6 7 8 9 10 11 12 Student Before 81 77 67 75 72 80 70 78 82 69 68 76 After 76 73 68 68 70 76 65 75 78 65 70 73 Send data to Excel Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Họ: (Choose one) H: (Choose one) This hypothesis test is a (Choose one) test.
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