Records of 40 used passenger cars and 40 used pickup trucks (none used commercially) were randomly selected to investigate whether there was any difference in the mean time in years that they were kept by the original owner before being sold. For cars the mean was 5.3 years with a population standard deviation, σ,2.2years. For pickup trucks the mean was 7.1 years with population standard deviation, σ,3.0years. Construct the 95% confidence interval for the difference in the means based on these data.

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Mike Henson · Accepted Answer

Step 1  3. Computation of critical value:  (1−α)=0.95  α=0.05  α2=0.025  1−α2=0.975  The critical value of z-distribution can be obtained using the excel formula “=NORM.S.INV(0.975)”. The critical value is 1.96.  Step 2  The 95% confidence interval for the difference in the means based on these data is,  Cl=(x―1−x―2)±zα2σ12n1+σ22n2  =(5.3−7.1)±1.962.2240+3.0240  =−1.8±(1.96×0.5882176)  =−1.8±1.1  =(−1.8−1.1,−1.8+1.1)  =(−2.9,−0.7)  Thus, the 95% confidence interval for the difference in the means based on these data is (-2.9, -0.7).

Records of 40 used passenger cars and 40 used pickup trucks (none used

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