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%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 2929 3636 2828 5050 2323 3737 3232 2929 4040 2121 Sit-ups after 4545 3838 3535 5656 4141 5555 4747 4545 4444 2626 Copy Data Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1x1 be the number of sit-ups before taking the course and x2x2 be the number of sit-ups after taking the course and use the formula d=x2−x1d=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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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%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	2929	3636	2828	5050	2323	3737	3232	2929	4040	2121
Sit-ups after	4545	3838	3535	5656	4141	5555	4747	4545	4444	2626

Copy Data

Step 1 of 4:

Find the point estimate for the population mean of the paired differences. Let x1x1 be the number of sit-ups before taking the course and x2x2 be the number of sit-ups after taking the course and use the formula d=x2−x1d=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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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