It has been suggested that night shiftworkers show more prod

It has been suggested that night shift-workers show more productivity in their output levels than day workers. Below, you are given the results of two small independent random samples. The management would like you to conduct a hypothesis test of the differences in means between these two groups. Night Shift Day Shift Sample Size 9 8 Sample Mean 520 540 Sample Variance 36 25

a. State the null and alternative hypotheses to be tested.

b. Compute the test statistic.

c. Determine the p-value

d. State your conclusion

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=520
Standard Deviation(s.d1)=6 ; Number(n1)=9
Y(Mean)=540
Standard Deviation(s.d2)=5; Number(n2)=8
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =520-540/Sqrt((36/9)+(25/8))
to =-7.49
| to | =7.49
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 7 d.f is 2.365
We got |to| = 7.49269 & | t | = 2.365
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -7.4927 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho