A ALEKS - Google ChromeA www-awu.connectmath.com/alekscgi/x/Isl.exe/1cqJCkxOUkfU30pEIASLkB2_hW4nmFZxw4EDq4u2zFQT1HSdvxh.. QSample QuestionObstacle Course Times An obstacle course was set up on a campus, and 11 volunteers were given a chance to complete it while they were beingtimed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in secondsare shown below. Is there sufficient evidence at a = 0.05 to conclude that the students did better the second time? Assume the variables arenormally distributed.Student134891011Before7078827569687681776772After6575786865707376736870Send 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 studentsdid 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) andD(E D²).Before (X)After (X2)Next, find the mean of the differences. D. snd the standardD=X-X,devistion of the differences. Sn7065525D =787539348278416- 3.0917568749nE D- (E Dn (n-1)69654166870-2411(174) - (34)11 (11 - 1)767338176525758V 110- 2.62577734166768-11Using the formula for the : test-for testing the differencebetween two means-dependent samples, compute the testvaluer727024Σ D= 34ED = 174Next, find the mean of the differences, D. and the standard deviation of the differences, Sn:3.091 -02.625//11EDD =- 3.905Hence, the test value rounded to three decimal places is-3.90534 Obstacle Course Times An obstacle course was set up on a campus, and 12 volunteers were given a chance to complete it whilethey 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 didbetter the second time? Assume the variables are normally distributed.123 4 56 7891011 12StudentBefore817767757280707882696876After767368687076657578657073Send data to ExcelPart: 0/5Part 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.

Question

A ALEKS - Google ChromeA www-awu.connectmath.com/alekscgi/x/Isl.exe/1cqJCkxOUkfU30pEIASLkB2_hW4nmFZxw4EDq4u2zFQT1HSdvxh.. QSample QuestionObstacle Course Times An obstacle course was set up on a campus, and 11 volunteers were given a chance to complete it while they were beingtimed. They then sampled a new energy drink and were given the opportunity to run the course again. The &#34;before&#34; and &#34;after&#34; times in secondsare shown below. Is there sufficient evidence at a = 0.05 to conclude that the students did better the second time? Assume the variables arenormally distributed.Student134891011Before7078827569687681776772After6575786865707376736870Send 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 studentsdid 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 &#34;the students did better the second time.&#34; 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) andD(E D²).Before (X)After (X2)Next, find the mean of the differences. D. snd the standardD=X-X,devistion of the differences. Sn7065525D =787539348278416- 3.0917568749nE D- (E Dn (n-1)69654166870-2411(174) - (34)11 (11 - 1)767338176525758V 110- 2.62577734166768-11Using the formula for the : test-for testing the differencebetween two means-dependent samples, compute the testvaluer727024Σ D= 34ED = 174Next, find the mean of the differences, D. and the standard deviation of the differences, Sn:3.091 -02.625//11EDD =- 3.905Hence, the test value rounded to three decimal places is-3.90534 Obstacle Course Times An obstacle course was set up on a campus, and 12 volunteers were given a chance to complete it whilethey were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The&#34;before&#34; and &#34;after&#34; times in seconds are shown below. Is there sufficient evidence at a= 0.05 to conclude that the students didbetter the second time? Assume the variables are normally distributed.123 4 56 7891011 12StudentBefore817767757280707882696876After767368687076657578657073Send data to ExcelPart: 0/5Part 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.

Accepted Answer

Given that 
An obstacle course was set up on a campus, and 12 volunteers were given a chance to…