Is this the correct interpretation of P-value?

[cloudy387]

The problem posed is this, skipping a lot of the exposition about what the test covers:

"A psychological test has a score range of 0 to 200. The mean score for US college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students score higher gives the test to 25 students who are at least 30 years of age. Their mean score is x̄ = 127.7. Assuming that σ = 30 for the population of older students, carry out a test of H₀: μ = 115 ; H_a: μ > 115. Report the P-value of your test and state your conclusion clearly."

z = (x̄ - μ₀) ÷ (σ/√n) = (127.8 - 115) ÷ (30/√25) = 2.133
H_a: μ > μ₀ is P(Z ≥ z) from which I calculate P(Z ≥ 2.133) = 1 - 0.9834 = 0.0166

My key question here is if my interpretation is correct:

1.66% of the time an SRS of size 25 from the general US college student population would have a mean score at least as high as that of the older student sample.

 

[Dr.Peterson]

The problem posed is this, skipping a lot of the exposition about what the test covers:

"A psychological test has a score range of 0 to 200. The mean score for US college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students score higher gives the test to 25 students who are at least 30 years of age. Their mean score is x̄ = 127.7. Assuming that σ = 30 for the population of older students, carry out a test of H₀: μ = 115 ; H_a: μ > 115. Report the P-value of your test and state your conclusion clearly."

z = (x̄ - μ₀) ÷ (σ/√n) = (127.8 - 115) ÷ (30/√25) = 2.133
H_a: μ > μ₀ is P(Z ≥ z) from which I calculate P(Z ≥ 2.133) = 1 - 0.9834 = 0.0166

My key question here is if my interpretation is correct:

1.66% of the time an SRS of size 25 from the general US college student population would have a mean score at least as high as that of the older student sample.

Look good to me, as an explanation of the p-value. You might also express it in terms of a sample from the older students, under the assumption that their mean is the same as for all students.

On the other hand, that may not be the "conclusion" they are asking for, which is often a statement about whether you think there is sufficient reason to reject the null hypothesis. You have to judge that based on how such questions are answered in your text or notes. Since there is some missing information in the problem, you may well be interpreting it correctly.

As I don't teach statistics, someone else may have a better answer.