A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, 2 hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of 5 vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. They would like to know if there is convincing evidence that the true mean run time differs from 2 hours. The consumer group plans to test the hypotheses ratio of cap h sub 0 to mu is equal to 2 versus ratio of cap h sub A to mu is less than 2 , where mu is equal to the true mean run time for all vacuums of this model. The power of this test to reject ratio of cap h sub 0 to mu is equal to 2 when mu is equal to 1 point 7 5 is 0 point 0 8 6 5 using a significance level of 0 point 0 5 Which combination of sample size and significance level would increase the power of this test the most?
Answer
A
n is equal to 10 , alpha is equal to 0 point 1 0
B
n is equal to 10 , alpha is equal to 0 point 0 1
C
n is equal to 20 , alpha is equal to 0 point 1 0
D
n is equal to 20 , alpha is equal to 0 point 0 1
Explanation
Power increases when the sample size is larger and the significance level α is higher. Increasing n from 5 to 20 gives more information about the mean, while increasing α from 0.05 to 0.10 makes it easier to reject the null hypothesis. Choice C, n = 20 and α = 0.10, combines both changes and therefore increases power the most. An α of 0.01 would instead make rejection harder and reduce power.
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