A state transport official claims that the mean waiting time at exit booths from a toll road near the capitol is no more than 0.40 minutes. For a sample of motorists exiting the toll road, it was found that the mean waiting time was 0.46 minutes, with a standard deviation of 0.16 minutes. At the 0.05 level of significance, can we reject the official's claim

How many were in the sample? z=\frac{(x-{\mu})\sqrt{n}}{\sigma}

H_{0}: {\mu}\leq .40, \;\ \text{claim}

H_{a}: {\mu}> .40

a right-tailed test.

If there is no sample size given, we can try this.

Test statistic: z=\frac{.46-.40}{.16}=.375

Using a .05 alpha level, the rejection region is z\geq 1.645

Clearly, 375 is not in the rejection region. Therefore, we fail to reject the null hypothesis.