Question

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. Using this data, find the 95% confidence interval for the true difference in the number of sit-ups each person can do before and after the course. Assume that the numbers of sit-ups are normally distributed for the population both before and after completing the course.

Sit-ups before   Sit-ups after
23   28
27   39
42   54
20   32
20   33
56   58
53   57
21   34
45   58
40   50

Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the rating from last year and x2 be the rating from this year and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

For step one I got 9.6

Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4: Construct the 95% confidence interval. Round your answers to one decimal place.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Mean = 9.6

Step - 2: Sample standard deviation = 4.248

Step - 3: Margin of error = (12.638747 - 6.561253)/2 = 3.038747

Step - 4: 95% confidence interval will be:

Lower limit = 6.6

Upper limit = 12.6