According to an April 28, 2015, report on the website newsroom.aaa.com, the average cost of owning and operating a sedan automobile in the United States in 2015 was $8,968.

Suppose the California AAA plans to conduct a survey to determine whether the average cost of owning a sedan in California is less than the $8,968 for the nation as a whole. Assuming that the population standard deviation for the cost of owning a sedan is $750, what is the probability that the hypothesis test will lead to accepting the null hypothesis if the true mean cost in California is actually $8,700.

a. State the null and alternative hypotheses.

b. Calculate the probability of a Type II error. Assume that the test is to be conducted using an alpha level of 0.01 and a sample size of 100 sedan owners.