Question

12) 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 $670. For 23 teenage girls, it was $564. 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.

Part (a)

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

Xboys − Xgirls ~ ( , )

Part (b) What is the test statistic? (If using the z distribution round your answer to two decimal places,

Part (c)

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

(ii) Explain what the p-value means for this problem.

a)If H0 is false, then there is a chance equal to the p-value that the sample average annual cost of insurance for boys is at least $106 more than the sample average cost for girls.

b)If H0 is true, then there is a chance equal to the p-value that the sample average annual cost of insurance for boys is $106 less than the sample average cost for girls.    

c)If H0 is true, then there is a chance equal to the p-value that the sample average annual cost of insurance for boys is at least $106 more than the sample average cost for girls.

d)If H0 is false, then there is a chance equal to the p-value that the sample average annual cost of insurance for boys is $106 less than the sample average cost for girls.

Part (d)

Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Answer 1