Given information
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 teenage boys was . For teenage girls, it was . 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.
Step-by-step explanation
The solution sheet provided for the problem is used to do the hypothesis testing as follows:
The null hypothesis can be stated as follows:
The alternate hypothesis can be stated as follows:
The random variable is the difference in the auto insurance of mean costs for boys and girls
The problem requires the Normal distribution.
To find the required statistic following algorithm is used:
- Press and twice to select the tests
- Press and to enter the stat list editor.
- Enter the given values as input as in the following display:
The output display is as follows:
The test statistic is .
Note the which is .
Using the previous information to sketch a picture of this situation. Labeled and scaled horizontal axis and shaded the region(s) corresponding to the The graph is,
The decisions and noted values are as follows:
Decision: The decision is to Reject the null hypothesis when .
Reason for Decision: .
Conclusion: At the level of significance, there is enough evidence to conclude that the mean cost of auto insurance for teenage boys is more than that for girls.
Hence, the hypothesis test is completed in format of given decision sheet.
The conclusion is to reject the null hypothesis and at the level of significance and there is enough evidence to conclude that the mean cost of auto insurance for teenage boys is more than that for girls.