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d) If the true mean is 4200, what sample size is needed if you do not wish for the Type II error rate to be greater than .25?

d) If the true mean is 4200, what sample size is needed if you do not wish for the Type II error rate to be greater than .25?

MATLAB: An Introduction with Applications
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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Thank you for answering a-c. Please answer part d.
Twenty randomly selected adults were given fitness trackers and the number of steps they took in one 24-hour period was measured. The researchers wish to test the following: Ho: µ =4000 vs HA: u > 4000 with a = .05. Assume that the number of steps people take per day is normally distributed with a known standard deviation of 500 steps. a) What is the probability of making a Type II error if the true mean number of steps people take in this population is 4200? What is the power of the test? b) If the true mean is greater than 4200, will the Type II error rate be lower, higher, or the same as in part a)? c) If the standard deviation were lower than 500 steps, would the Type II error rate be lower, higher, or the same as in part a)? d) If the true mean is 4200, what sample size is needed if you do not wish for the Type II error rate to be greater than .25?
Transcribed Image Text:Twenty randomly selected adults were given fitness trackers and the number of steps they took in one 24-hour period was measured. The researchers wish to test the following: Ho: µ =4000 vs HA: u > 4000 with a = .05. Assume that the number of steps people take per day is normally distributed with a known standard deviation of 500 steps. a) What is the probability of making a Type II error if the true mean number of steps people take in this population is 4200? What is the power of the test? b) If the true mean is greater than 4200, will the Type II error rate be lower, higher, or the same as in part a)? c) If the standard deviation were lower than 500 steps, would the Type II error rate be lower, higher, or the same as in part a)? d) If the true mean is 4200, what sample size is needed if you do not wish for the Type II error rate to be greater than .25?
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