1. 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 Can the
supervisor conclude at the 5% significance level that the
assumption that the mean assembly time is 130 seconds
is correct?

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

3. 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.