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Problem

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9 Dec 2021

Given information

Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test  hybrid sedans and get a mean of  mpg with a standard deviation of seven mpg. Thirty one non-hybrid sedans get a mean of  mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test to evaluate the manufacturers claim.

Step-by-step explanation

Step 1.

The hypothesis testing in the required format as given in the problem is as follows:

 The null hypothesis can be stated as follows:

       

 The alternate hypothesis can be stated as follows:

    

The random variable is defined as the difference between the mean miles per gallon of non-hybrid sedans and hybrid sedans.

The normal distribution is applicable.

 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 .    

 The  is , as displayed in the output.  

 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 null hypothesis.

        Reason for Decision: Because, .

        Conclusion: At the  level of significance, there is enough evidence to conclude that the mean miles per gallon of non-hybrid sedans is less than that of                    hybrid sedans.

 

Hence, the hypothesis test is completed in format of given decision sheet.

The conclusion is not to reject the null hypothesis and at the  level of significance because there is enough evidence to conclude that the mean miles per gallon of non-hybrid sedans is less than that of hybrid sedans.

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