Example 3: Brandon runs a local gym and was interested in determining how many hours per week on average his members spend working out. He randomly sampled 72 of his members and found that they spent an average of 11.4 hours per week working out. Assume it is known that the true standard deviation is 3.6 hours. a) Construct and interpret an 85% confidence interval for the true average number of hours per week that Brandon's members spend working out. b) How would the interval that you created in part (a) compare to an 80% confidence interval for the same parameter? Calculate the new interval to justify your answer. c) How would the interval that you created in part (a) compare to a 95% confidence interval for the same parameter? Calculate the new interval to justify your answer.

Example 3: Brandon runs a local gym and was interested in determining how many hours per week on average his members spend working out. He randomly sampled 72 of his members and found that they spent an average of 11.4 hours per week working out. Assume it is known that the true standard deviation is 3.6 hours. a) Construct and interpret an 85% confidence interval for the true average number of hours per week that Brandon's members spend working out. b) How would the interval that you created in part (a) compare to an 80% confidence interval for the same parameter? Calculate the new interval to justify your answer. c) How would the interval that you created in part (a) compare to a 95% confidence interval for the same parameter? Calculate the new interval to justify your answer.

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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Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

Example 3: Brandon runs a local gym and was interested in determining how many hours per
week on average his members spend working out. He randomly sampled 72 of his members and
found that they spent an average of 11.4 hours per week working out. Assume it is known that
the true standard deviation is 3.6 hours.
a) Construct and interpret an 85% confidence interval for the true average number of hours
per week that Brandon's members spend working out.
b) How would the interval that you created in part (a) compare to an 80% confidence interval
for the same parameter? Calculate the new interval to justify your answer.
c) How would the interval that you created in part (a) compare to a 95% confidence interval
for the same parameter? Calculate the new interval to justify your answer.

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