H0: μ =3100, Ha: μ≠3100. We should use a two-tailed test because μ≠3100 includes values both larger and smaller than 3100.
At a 5% level of significance, decision rule is to reject Ho if the z score is outside the range -1.96 to 1.96.
Under H0, μ =3100 and using samples standard deviation as an estimate of σ. Since Z=(Xbar-μ0)/(σ/√n)=(3200-3100)/(250/) = 100/50=2.00, which lies outside the range -1.96 to 1.96, we reject H0 at 5% level of significance. While it is close, the evidence suggests that the mean time until major repair is greater than 3,100 hours