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 99%

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	40

51

52

30

44

34

34

49

36

44

Sit-ups after	56

53

57

43

59

44

46

53

54

57

Step 1 of 4:Find the point estimate for the population mean of the paired differences. Let x1

be the number of sit-ups before taking the course and x2 be the number of sit-ups after taking the course and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

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 99%

confidence interval. Round your answers to one decimal place.

Answer 1

Step 1 of 4:  point estimate =10.8

Step 2 of 4: sample standard deviation =5.432413

Step 3 of 4:

for 99% CI; and 9 degree of freedom, value of t=			3.250
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		5.583109

step 4:

lower confidence limit                     =		5.2
upper confidence limit                    =		16.4