The maker of a certain model car claimed that hiscar averaged 31 miles per gallo

Question

The maker of a certain model car claimed that hiscar averaged 31 miles per gallon of gasoline with a standarddeviation of 1 (based on a sample size of 1000). A sample of ninecars was selected and each car was driven with one gallon ofregular gasoline. The sample showed a mean of 29.43 miles with astandard deviation of 3 miles. ( = .05

What do you conclude about the manufacturersclaim? Df = 8

If the same results were obtained with a samplesize of 25 would you conclude the same thing?

Explanation / Answer

=31, =1 n=9, xbar=29.43, s=3 =0.05, t(0.025,df=n-1=8)=-2.31 The test hypothesis is Ho:=31 Ha: not equal 31 The test statistics is t=(xbar-)/(s/n)= (29.43-31)/(3/sqrt(9))=-1.57 Since t=-1.57> -2.31, do not reject Ho. If the sample size is 25, then the test statistics is Z=(29.43-31)/(3/sqrt(25)) =-2.62. =0.05, Z(0.025)=-1.96 Since Z=-2.62 < -1.96, reject Ho.

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