Example 5 The supervisor of a production line that assembles computer keyboards has been experiencing problems since a new process was instituted. He notes that there has been an increase in defective units and occasional backlogs when one station’s productivity is not matched by the other stations’. Upon reviewing the process, the supervisor discovered that the management scientists who developed the production process assumed that the amount of time to complete a critical part of the process is normally distributed with a mean of 130 seconds and a standard deviation of 15 seconds. He is satisfied that the process time is normally distributed with a standard deviation of 15 seconds, but he is unsure about the mean time. In order to examine the problem, he measures the times for 100 assemblies. The mean of these times was calculated to be 126.8. Can the supervisor conclude at the 5% significance level that the assumption that the mean assembly time is 130 seconds is correct?

Outline of Solution Test statistic : Rejection region : Value of the test statistic : continued

Conclusion: Since ,which is greater than 1.96, reject the null hypothesis and conclude that there is enough evidence to infer that the mean time is not equal to 130 seconds.