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)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=0.01 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	21	33	29	30	27	49	30	21	49	41
Sit-ups after	35	40	43	42	34	53	46	36	51	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: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

Answer 1

Step 1: H0: Participation in the physical fitness course resulted in not significant improvement

H0: Participation in the physical fitness course resulted in significant improvement (One tailed test)

Step 2:From the given data

Step 4:

Critical t:              2.8214
P-Value:                 0.0002

since t value > t critical value and P-value < alpha 0.01 so we reject H0

Step 5: Thus we conclude that there is sufficient evidence that Participation in the physical fitness course resulted in significant improvement