A Researcher Wishes to Determine If Aerobic Exercise Improves Mental

Multiple Choice

A researcher wishes to determine if aerobic exercise improves mental performance immediately following the exercise. He plans to have high school students participate in 30 minutes of aerobic exercise and then take a standard test of their reasoning skills. Suppose the scores of high school students on this test of reasoning skills immediately after 30 minutes of aerobic exercise follow a Normal distribution, with mean μ and standard deviation σ= 4. Suppose also that, in the general population of all high school students, scores on the test of reasoning skills follow a Normal distribution, with mean 25 and standard deviation σ= 4. The researcher, therefore, decides to test the following hypotheses:
H₀: μ= 25, H_a: μ> 25
To do so, the researcher has 10,000 high school students perform 30 minutes of aerobic exercise and then, immediately following the exercise, take the test. The mean score for these students is x̄= 25.2 and the P-value is less than 0.0001.
Suppose that two high school students decide to see if they get the same results as the researcher. They both do 30 minutes of aerobic exercise and, immediately following the exercise, take the test. The mean of their scores is = 25.2 seconds, the same as that of the researcher. It is appropriate to conclude which of the following?

A) They have reproduced the results of the researcher, and their P-value will be the same as that of the researcher.
B) They have reproduced the results of the researcher, but their P-value will be slightly smaller than that of the researcher.
C) They will reach the same statistical conclusion as the researcher, but their P-value will be a bit different than that of the researcher.
D) None of these options is correct.