An agency that hires out clerical workers claims its workers can type, on average, at least 60 words per minute (wpm
). 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 wpm
. A one-sample t-test was conducted to investigate whether there is evidence that the mean typing speed of workers from the agency is less than 60 wpm
. The resulting p-value was 0.267.
Which of the following is a correct interpretation of the p
p
-value?
The probability is 0.267 that the mean typing speed is 60 wpm
or more for workers from the agency.
A
The probability is 0.267 that the mean typing speed is 60 wpm
or less for workers from the agency.
B
The probability is 0.267 that the mean typing speed is 58.8 wpm
or less for workers from the agency.
C
If the mean typing speed of workers from the agency is 60 wpm
, the probability of selecting a sample of 50 workers with mean 58.8 wpm
or less is 0.267.
D
If the mean typing speed of workers from the agency is less than 60 wpm
, the probability of selecting a sample of 50 workers with mean 58.8 wpm
or less is 0.267.
E
Is E correct?
A
No, E is not correct. The p-value does not provide information about the direction of the difference between the sample mean and the hypothesized value, only the strength of evidence against the null hypothesis.
Yes, the correct interpretation of the p-value in this situation is:
E) If the mean typing speed of workers from the agency is less than 60 wpm, the probability of selecting a sample of 50 workers with a mean of 58.8 wpm or less is 0.267.
This interpretation aligns with the hypothesis being tested, which is whether there is evidence that the mean typing speed of workers from the agency is less than 60 wpm. The p-value gives the probability of obtaining the observed sample mean (58.8 wpm) or a more extreme value, given that the true mean is less than 60 wpm. If the p-value is low (usually less than 0.05), it is interpreted as evidence against the null hypothesis (in this case, the null hypothesis being that the mean typing speed is 60 wpm). In this case, with a p-value of 0.267, there is not enough evidence to reject the null hypothesis.