Question

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced by a sample of 52 day-shift workers was 322. The mean number of units produced by a sample of 56 night-shift workers was 331. Assume the population standard deviation of the number of units produced on the day shift is 18 and 28 on the night shift.

At the 0.02 significance level, is the number of units produced on the night shift larger?

2. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Answer 1

b)

H0: D = N

Ha: D < N

This is left tailed test.

Critical value at 0.02 level = -2.05

Decision rule = Reject H0 if test statistics z < -2.05

c)

Test statistics

z = (D - N) / sqrt [ D / n + N / n ]

= (322 - 331) / sqrt ( 18² / 52 + 28² / 56 )

= -2.00