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 327. The mean number of units produced by a sample of 58 night-shift workers was 332. Assume the population standard deviation of the number of units produced on the day shift is 23 and 31 on the night shift. At the 0.05 significance level, is the number of units produced on the night shift larger? Is this a one-tailed or a two-tailed test? One-tailed test Two-tailed test State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0. Do not reject H0.

Answer 1

Day shift denoted by D and night shift denoted by N. mean and variance of day and night shifts denoted by muD, muN, vD, vN.

For determining whether it is a one tailed or two tailed test, first we make hypothesis-

null hypothesis- H0= number of units produced on night shifts is equal to number of units       produced on day shifts.

altenative hypothesis- H1=number of units produced on night shifts is more than number of units produced on day shifts.

By alternative hypotheisis , we can say that it is one tailed test.

Z=(muD-muN)/sqrt((vD/n1)+(vN/n2))

muD=327, n1=52, vD=(23)^2

muN=332, n2=58, vN=(31)^2

z=(-5)/sqrt(10.17+16.56)=(-5)/sqrt(26.73)

z=-5/5.17= -0.96

|z|=0.96<1.96, there is no evidence against null hypothesis. So we can't reject the null hypothesis. This means, number of units produced on night shifts is equal to number of units      produced on day shifts.