An SRS of 100 postal employees found that the average time these employees had worked at the postal service was $7$ years with standard deviation $2$ years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of $7.5$ that was true $20$ years ago? To determine this, we test the hypotheses $H_{0} : μ = 7.5$ versus $H_{a} : μ \neq 7.5$ using a one-sample $t$ test. What conclusion should we draw at the $5 %$ significance level?
(a) There is convincing evidence that the mean time working with the postal service has changed.
(b) There is not convincing evidence that the mean time working with the postal service has changed.
(c) There is convincing evidence that the mean time working with the postal service is still $7.5$ years.
(d) There is convincing evidence that the mean time working with the postal service is now $7$ years.
(e) We cannot draw a conclusion at the $5 %$ significance level. The sample size is too small.

Question

Accepted Answer

The answer is (a). There is convincing evidence that the mean time working with the postal service has changed.

Short Answer