Thank you for answering a-c. Please answer part d. Twenty randomly selected adults were given fitness trackers and the number of steps they tookin one 24-hour period was measured. The researchers wish to test the following: Ho: µ =4000 vsHA: u > 4000 with a = .05. Assume that the number of steps people take per day is normallydistributed 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 takein 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 sameas 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 errorrate to be greater than .25?

d. Given information: Formula for Type II error is Given that the type II error rate to be not…

Answered: d) If the true mean is 4200, what…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.5: Comparing Sets Of Data

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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?

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