A public bus company official claims that mean waiting time for bus number 14 throughout peak hours is 10 minutes. Karen took bus number 14 during peak hours on 18 randomly selected days. Her mean waiting time was 8 minutes.
Do the data provide sufficient evidence to conclude that mean waiting time differs from 10 minutes claimed by the bus company? Suppose that the population standard deviation of waiting times is 2.2 minutes. Employ the following steps to answer the question.
a. Describe the null and alternative hypotheses.
b. Explain the logic of conducting the hypothesis test.
c. Determine the distribution of the variable x , that is, the sampling distribution of the mean for samples of size 18.
d. Obtain a precise criterion for deciding whether to reject the null hypothesis in favor of the alternative hypothesis.
e. Apply the criterion in part (d) to the sample data and state your conclusion.