Clark Heter is an industrial engineer at Lyons Products He w

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift rather than on the day shift. A sample of 60 day-shift workers showed that the mean number of units produced was 352, with a population standard deviation of 24. A sample of 64 night-shift workers showed that the mean number of units produced was 362, with a population standard deviation of 31 units. At the .02 significance level, is the number of units produced on the night shift larger? This is a -tailed test. The decision rule is to reject H_0 : mu d greater than or equal to mu n if Z less than . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) The test static is Z = (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H_0?

Solution

Set Up Hypothesis
Null , Ho: Ud >= Un
Alternate , H1: Ud < Un
Test Statistic
X(Mean)=352
Standard Deviation(s.d1)=24
Number(n1)=60
Y(Mean)=362
Standard Deviation(s.d2)=31
Number(n2)=64
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=352-362/Sqrt((576/60)+(961/64))
Zo =-2.02
| Zo | =2.02
Critical Value
The Value of |Z | at LOS 0.02% is 2.054
We got |Zo | =2.016 & | Z | =2.054
Make Decision
Hence Value of | Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -2.02 ) = 0.02192
Hence Value of P0.02 < 0.02192,Here We Do not Reject Ho

[ANSWERS]
1.one tailed
2.Reject Ho, Ud>=Un, if Z<-2.054
3.Zo =-2.02
4.Do not Reject Ho