Question

A company produces a single product on three production lines that use different equipment. The production manager is considering changing the layouts of the lines and would like to know what effects different layouts would have on production output. Suppose that the manager measured the average output for each line over three randomly selected weeks using each of the three layouts under consideration. The output​ (in hundreds of units​ produced) was measured for each line for each of the four weeks for each layout being evaluated. The results are shown in the accompanying table. Complete parts a through c below.

Data Table Line 1 Line 2 Line 3 Layout 1 10 O 12 20 Layout 2 22 36 19 33 Layout 3 40 39 28 36 40 31

Answer 1

using excel>data>data analysis>ANOVA with replication

we have

Anova: Two-Factor With Replication
SUMMARY	Line 1	Line 2	Line 3	Total
Layout 1
Count	3	3	3	9
Sum	27	42	61	130
Average	9	14	20.33333	14.44444
Variance	21	28	105.3333	62.77778
Layout 2
Count	3	3	3	9
Sum	56	72	94	222
Average	18.66667	24	31.33333	24.66667
Variance	86.33333	39	32.33333	69.75
Layout 3
Count	3	3	3	9
Sum	93	108	106	307
Average	31	36	35.33333	34.11111
Variance	67	48	16.33333	38.36111
Total
Count	9	9	9
Sum	176	222	261
Average	19.55556	24.66667	29
Variance	134.7778	119.75	83.75
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Layout	1741.407	2	870.7037	17.67594	5.66E-05	3.554557
Lines	402.2963	2	201.1481	4.083459	0.034489	3.554557
Interaction	78.14815	4	19.53704	0.396617	0.808423	2.927744
Within	886.6667	18	49.25926
Total	3108.519	26

a ) the null and alternative hypothesis are given by option C

p value is 0.808

since p value is greater than 0.025 so we do not reject Ho

option C is true

b ) the null and alternative hypothesis are given by option A

p value is 0.035

since p-value is greater than 0.025 so we do not reject Ho

option C is true

c )

the null and alternative hypothesis are given by option A

p value is 0.000

since p-value is less than 0.025 so we reject Ho

option B is true