a social scientist collects information about...

a social scientist collects information about study time for a random sample of 40 students with the intention of testing the hypotheses $h_0: mu = 2$ hours per night versus $h_a: mu\neq2$ hours per night where $mu$ = the true mean number of hours of study time per night for students. the power of this test to reject the null hypothesis when $mu = 2.25$ is 0.35. what is the correct interpretation of the value 0.35?\nthe probability that this test will reject that the true mean number of hours of study time per night for students is 2 when the true mean is not 2.25 is 0.35.\nthe probability that this test will reject that the true mean number of hours of study time per night for students is 2 when the true mean is really 2.25 is 0.35.\nthe probability that this test will fail to reject that the true mean number of hours of study time per night for students is 2 when the true mean is not 2.25 is 0.35.\nthe probability that this test will fail to reject that the true mean number of hours of study time per night for students is 2 when the true mean is really 2.25 is 0.35.

Answer

# Brief Explanations: The power of a hypothesis - test is the probability of correctly rejecting the null hypothesis. Here, the null hypothesis is $H_0:\mu = 2$ and we are considering the situation when the true mean $\mu = 2.25$. A power of 0.35 means the probability of rejecting the null hypothesis ($\mu = 2$) when the true mean is 2.25 is 0.35. # Answer: The probability that this test will reject that the true mean number of hours of study time per night for students is 2 when the true mean is really 2.25 is 0.35.