A fitness course claims that it can improve an individual'sphysical ability. To test the effect of a physical fitness courseon one's physical ability, the number of sit-ups that a personcould do in one minute, both before and after the course, wasrecorded. Ten individuals are randomly selected to participate inthe course. The results are displayed in the following table. Canit be concluded, from the data, that participation in the physicalfitness course resulted in significant improvement? Let d=(numberof sit-ups that can be done after taking the course)−(number ofsit-ups that can be done prior to taking the course) . Use asignificance level of α=0.01 for the test. Assume that the numbersof sit-ups are normally distributed for the population both beforeand after taking the fitness course.
| Sit-ups before | 20 | 38 | 24 | 26 | 38 | 55 | 23 | 42 | 44 | 44 |
| Sit-ups After | 36 | 43 | 26 | 37 | 50 | 58 | 38 | 51 | 59 | 49 |
Step 1 of 5 : State the null and alternative hypotheses for thetest.
Step 2 of 5: Find the value of the standard deviation of thepaired differences. Round your answer to one decimal place.
Step 3 of 5: Compute the value of the test statistic. Round youranswer to three decimal places.
Step 4 of 5: Determine the decision rule for rejecting the nullhypothesis H0. Round the numerical portion of your answer to threedecimal places.
Step 5 of 5: Make the decision for the hypothesis test.
