Question

An agency that hires out clerical workers claims its workers can type, on average, at least 60 words per minute (wpmwpm). To test the claim, a random sample of 50 workers from the agency were given a typing test, and the average typing speed was 58.8 wpmwpm. A one-sample tt-test was conducted to investigate whether there is evidence that the mean typing speed of workers from the agency is less than 60 wpmwpm. The resulting pp-value was 0.267.

Which of the following is a correct interpretation of the pp-value?

The probability is 0.267 that the mean typing speed is 60 wpmwpm or more for workers from the agency.

A

The probability is 0.267 that the mean typing speed is 60 wpmwpm or less for workers from the agency.

B

The probability is 0.267 that the mean typing speed is 58.8 wpmwpm or less for workers from the agency.

C

If the mean typing speed of workers from the agency is 60 wpmwpm, the probability of selecting a sample of 50 workers with mean 58.8 wpmwpm or less is 0.267.

D

If the mean typing speed of workers from the agency is less than 60 wpmwpm, the probability of selecting a sample of 50 workers with mean 58.8 wpmwpm or less is 0.267.

E

Answer 1

The right answer is:

If the mean typing speed of workers from the agency is 60 wpmwpm, the probability of selecting a sample of 50 workers with mean 58.8 wpmwpm or less is 0.267.

Explanation:

The P-value gives us the probability of getting the sample we are evaluating (in this case a sample with size n=50 and mean=58.8 wpm), if the null hypothesis is true (in this case, μ=60 wpm).

If the P-value is low enough, that is under the significance level, then we can infer that the mean that the null hypothesis states is not the actual mean, and we have evidence to reject the null hypothesis.