A Researcher Wishes to Determine If Aerobic Exercise Improves Mental

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. It is appropriate to conclude which of the following?

A) The researcher has conclusively proved that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance.
B) The researcher has strong evidence that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance.
C) The researcher has moderate evidence that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance.
D) None of these options is correct.