A certain test preparation course is designed to help students improve their scores on the GMAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course:

27,21,10,29,12

Using these data, construct a 99% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.

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Step 1 of 4:

Calculate the sample mean for the given sample data. Round your answer to one decimal place Step 2 of 4:

Calculate the sample standard deviation for the given sample data. Round your answer to one decimal place.

Step 3 of 4:

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 4 of 4:

Construct the 99% confidence interval. Round your answer to one decimal place.