Question

The labor charge for repairs at an automobile service center are based on a standard time specified for each type of repair. The time specified for replacement of universal joint in a drive shaft is one hour. The manager reviews a sample of 30 such repairs. The average of the actual repair times is 0.86 hour with standard deviation 0.32 hour.

1. Test at the 1% level of significance the null hypothesis that the actual mean time for this repair differs from one hour.
2. The sample mean is less than one hour, suggesting that the mean actual time for this repair is less than one hour. Perform this test, also at the 1% level of significance. (The computation of the test statistic done in part (a) still applies here.)

Answer 1

a)

H0: = 1 ,

H1: 1

Test statistics

t = - / (S / sqrt(n) )

= 0.86 - 1 / (0.32 / sqrt(30) )

= -2.40

This is test statistics value.

t critical value at 0.01 level with 29 df = -2.756, 2.756

Since test statistics value falls in non-rejection region, we do not have sufficient evidence to reject the

null hypothesis.

We conclude at 0.01 level that we fail to support the claim.

b)

H0: = 1 ,

H1: < 1

Test statistics

t = ​​​​​​​ - / (S / sqrt(n) )

= 0.86 - 1 / (0.32 / sqrt(30) )

= -2.40

This is test statistics value.

t critical value at 0.01 level with 29 df = -2.462

Since test statistics value falls in non-rejection region, we do not have sufficient evidence to reject the

null hypothesis.

We conclude at 0.01 level that we fail to support the claim.