Question

Test the ability of auto mechanics to identify simple engine problems, an automobile with a single suchproblem was taken to 72 different car repair facilities. Only 42 out of 72 mechanics who worked on the carcorrectly identified the problem. Does this strongly indicate that the true proportion of mechanics who couldidentify this probelm is less than.75? Compute the p-value and reach a conclusion.

Answer 1

The proportion is less than 0.75 only

Explanation:

given that the ability of auto mechanics to identify simple engine problems, an automobile with a single suchproblem was taken to 72 different car repair facilities.

Sample proportion
`= 42/72=0.5833`

Set up hypotheses as

H0: p =0.75

Ha: p < 0.75

(Left tailed test)

Assuming H0 to be true, std error of proportion =
`\sqrt{(0.75*0.25)/(72) } \\=0.0668`

p difference = -0.1667

Test statistic Z = p diff/std error = -2.50

p value = 0.0062

since p is less than0.05 at 5% significance level we reject null hypothesis

The proportion is less than 0.75 only