Question

Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $673. For 23 teenage girls, it was $558. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls. Conduct a hypothesis test at the 5% level.

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (d) State the distribution to use for the test. (Round your answers to two decimal places.)

X_boys − X_girls ~. _______. (. , )

Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

Part (f) What is the p-value? (Round your answer to four decimal places.)

Answer 1