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=0.05 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 51 45 32 42 33 29 33 56 36 24 Sit-ups after 58 57 37 45 44 42 41 58 45 41 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 H 0 . Round the numerical portion of your answer to three decimal places. Step 5 of 5.accept or reject null

Answer 1

The statistical software output for this problem is:

From above output:

Step - 1: Ho:

Ha:

Step - 2: Standard deviation = 4.692

Step - 3: Test statistic = 5.864

Step - 4: Reject Ho if t > 1.833

Step - 5: Reject Null Hypothesis