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Problem

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9 Dec 2021

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

Step 1.

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:

  1. Press  and twice  to select the tests
  2. Press  and  to enter the stat list editor. 
  3. 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.

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