A personal trainer determines that an individual will get the most benefit from a workout if they keep their heart rate at an average of 150 beats per minute during workouts. To determine if the individual is doing so successfully, a random sample of 30 workouts is selected from their fitness watch. A 95 percent confidence interval for these workouts reveals that the true mean heart rate while working out is between 158 and 167 beats per minute. Based upon this interval, what conclusion should be made about the hypotheses: ratio of cap h sub 0 to mu is equal to 150 versus ratio of cap h sub A to mu is not equal to 150 where μ= this individual’s true mean heart rate during working out at α=0.05 ?
Answer
A
Reject cap h sub 0 . There is convincing evidence that this individual’s true mean heart rate while working out differs from 150 .
B
Reject cap h sub 0 . There is convincing evidence that the mean heart rate from these 30 workouts differs from 150 .
C
Fail to reject cap h sub 0 . There is not convincing evidence that the mean heart rate from these 30 workouts differs from 150 .
D
Fail to reject cap h sub 0 . There is not convincing evidence that this individual’s true mean heart rate while working out differs from 150 .
Explanation
The 95% confidence interval for the individual’s true mean heart rate is 158 to 167 beats per minute, and 150 is not in that interval. For a two-sided test at α = 0.05, this means we reject H₀: μ = 150 and have convincing evidence that the individual’s true mean heart rate differs from 150. Choice A states this conclusion about the true mean, rather than only about the 30 sampled workouts.
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