Question

Randomly selected college students were selected to test their ability to determine when 1 minute has passed. Forty students yielded a sample mean of 58.3 seconds. Assuming that sigma = 9.5, use a 0.05 significance level to test the claim that the population mean is equal to one minute.

Answer 1

\[H _{0}:\ \mu=60\ seconds\]
\[H _{a}:\ \mu<\mu _{0}\]
The test statistic is found from:
\[Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{58.3-60}{\frac{9.5}{\sqrt{40}}}=-1.132\]
At a significance level of 0.05 the critical value is -1.645. Since the test statistic does not lie in the rejection region Z < -1.645, we cannot reject the null hypothesis in favor of the alternative at the 0.05 significance level.