Question

To reach maximum efficiency in performing an assembly operation at a manufacturing plant, new employees require approximately a 1-month training period. A new method of training was suggested, and you are tasked with testing whether the new method is more efficient than the standard procedure. Two groups of 30 new employees each were trained for a period of 3 weeks, one group using the new method and the other following the standard training procedure. The length of time (in minutes) required for each employee to assemble the device was recorded at the end of the 3-week period. Assume that the assembly times are approximately normally distributed with means µ1 (old method) and µ2 (new method), that the variances of the assembly times are approximately equal to 4 minutes for both methods, and that the samples are independent.

1. How would you state the hypothesis testing problem in this case? What is the null and what is the alternative?

2. How would you test the hypothesis? Define the test statistic and the rejection region for an arbitrary significance level.

3. Find the sample size n so that both the type-I and the type-II errors of the test against the alternative µ1 − µ2 = 2 are less than 0.1. You can leave the answer in terms of a formula for n

Answer 1

a) Null Hypothesis: The stat does not presentsufficient evidence to indicate that the mean time to assemble atthe end of a 3 week training period is less for the new trainingprocedureAlternative Hypothesis: the stat present sufficientevidence to indicate that the mean time to assemble at the end of a3 week training period is less for the new trainingprocedure

By using the given data we have to find out thesample mean and sample standard deviation

                 NMean    StDev

Standard procedu 9 35.22  4.94

New procedure    9 31.56  4.48

The test statistic is given by