Question

A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement?  

Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course). Use a significance level of α=0.1 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course.

Sit-ups before 28 48 25 41 23 25 45 21 37 29

Sit-ups after 40 54 43 55 34 42 52 30 49 43

Step 1 of 5 : State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Find the p-value for the hypothesis test. Round your answer to four decimal places.

Step 5 of 5: Draw a conclusion for the hypothesis test.

Answer 1

Step 1 of 5 :

null Hypothesis:		μd	=	0
alternate Hypothesis:		μd	>	0

Step 2 of 5: value of the standard deviation =3.944

Step 3 of 5: Compute the value of the test statistic =9.730 ( please try 9.621 if this comes wrong)

Step 4 of 5: Find the p-value for the hypothesis test =0.0000

Step 5 of 5: reject null and conclude that participation in the physical fitness course resulted in significant improvement