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 90% 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 44 33 40 32 21 35 52 24 32 48

Sit-ups after 58 36 53 40 37 39 58 38 36 60

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 90% confidence interval. Round your answers to one decimal place.

Answer 1

step 1:  point estimate for the population mean =9.4

step2 : sample standard deviation =4.926121

Step 3 of 4:

for 90% CI; and 9 degree of freedom, value of t=			1.833
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		2.855404

step 4:

lower confidence limit                     =		6.5
upper confidence limit                    =		12.3