CarMD reports that the cost of repairing a hybrid vehicle is falling even while

Question

CarMD reports that the cost of repairing a hybrid vehicle is falling even while typical repairs on conventional vehicles are getting more expensive. The most common hybrid repair, replacing the hybrid inverter assembly, had a mean repair cost of $3,927 in 2012. Industry experts suspect that the cost will continue to decrease given the increase in the number of technicians who have gained expertise on fixing gas–electric engines in recent months. Suppose a sample of 100 hybrid inverter assembly repairs completed in the last month was selected. The sample mean repair cost was $3,800 with the sample standard deviation of $500. Is there evidence that the population mean cost is less than $3,927? (Use a 0.05 level of significance.)

Explanation / Answer

here null hypothesis: mean >=3927

alternate hypothesis: mean <3927

std error=std deviation/(n)1/2 =50

hence test stat t=(X-mean)/std error =(3800-3927)/50=-2.54

for above test stat p value =0.0063

as p value is less then 0.05 level we reject null hypothesis and conclude that the population mean cost is less than $3,927

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