Question

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 25 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At significance levels of .05, test whether the completion time has increased. (construct the hypotheses, show the critical and calculated values of the test statistic and perform test)

Answer 1

H0: <= 6

Ha: > 6

Test statistics

t = - / S / sqrt(n)

= 6.5 - 6 / 1.5 / sqrt(25)

= 1.67

This is test statistics value.

Critical value at 0.05 level with 24 df = 2.492

Since test statistics falls in non-rejection region, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim.