Question

Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift.

At the 0.05 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?

Units Produced Employee Day Afternoon Night

Skaff 31 21 34

Lum 33 25 37

Clark 27 28 38

Treece 33 22 28

Morgan 25 24 36

What is your decision regarding H0? (Round your answers to 2 decimal places.) What is your conclusion?

Answer 1

Here, N = 15 ( NO. OF EMPLOYEES * TIMES = 5 * 3)

k = 3 ( Timings)

The null hypothesis is :

H₀: There is no significant difference in the mean production rate by shift or by employee i.e.

The alternative hypothesis is:

H₁: There is a significant difference in the mean production rate by shift or by employee i.e.

31	33	27	33	25	961	1089	729	1089	625
21	25	28	22	24	441	625	784	484	576
34	37	38	28	36	1156	1369	1444	784	1296

Grand Total =

Total Sum Of Squares (TSS) =

=

= 2558 + 3083 + 2957 + 2357 + 2497 - [442²/15]

= 427.73

Sum of squares between classes (SST) =

=

=

= 37.07

Sum of Squares within classes (SSE) = TSS - SST = 427.73 - 37.07 = 390.66

The ANOVA table:

Sources of Variation	Sum Of Squares	Degree of Freedom	Mean Sum Of Squares	F-Statistic
Between Classes	SST	k -1	SST/ (k-1) = MST	MST/MSE
Within Classes	SSE	N - k	SSE / (N - k) = MSE
Total	TSS	N - 1

Putting the values in ANOVA Table:

Sources of Variation	Sum Of Squares	Degree of Freedom	Mean Sum Of Squares	F-Statistic
Between Classes	37.07	2	18.535	0.57
Within Classes	390.66	12	32.55
Total	427.73	14

Now, The Tabulated value of F-statistic (see the image below) at (2,12) degrees of freedom at 5% level of significance is 3.88. Since calculated value of F is less than tabulated value of F, therefore H₀ is accepted at 5% level of significance.

Hence , there is no significant difference in the mean production rate by shift or by employee.