A randomized comparative experiment examined the effect of a technique for impro

Question

A randomized comparative experiment examined the effect of a technique for improving one’s ability to focus one’s attention on performance of undergraduate students on the Verbal portion of the Graduate Record Exam (GRE). The researchers found a statistically significant improvement in performance on the Verbal GRE (P < 0.05). When asked to explain the meaning of the P-value was P = 0.03, a student says, This means there is only probability 0.03 that the null hypothesis is true. When asked to explain the meaning of (P < 0.05),” a student says, “This means there is only probability less than 0.05 that the null hypothesis is true.” Explain what P = 0.05 really means in a way that makes it clear that the student's explanation is wrong.

A) P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05.

B) P = 0.05 means that the outcome is at least 5% higher among one group than among the other group.

C) P = 0.05 means that there is a probability of 0.05 that the null hypothesis is false.

D) P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is less than 0.05.

Explanation / Answer

The correct interpretation is

OPTION A: A) P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05. [ANSWER]

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Note that in any hypothesis test, we assume first that the null hypothesis is true. Now, if we get the P value, it is the probability that we would get a sample at least as rare as the sample ge got. If it is small, then all the more we have reasons not to believe the null hypothesis.

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