Question

Three manufacturing companies supply consumables to a large corporation in batches of
300 units. Random samples of six recently supplied batches from each of the three
suppliers were carefully checked, and the numbers of parts not conforming to standards
were recorded. These numbers are listed in the table below:

Supplier A	Supplier B	Supplier C
28	22	33
37	27	29
34	29	39
29	20	33
31	18	37
33	30	38

a) Prepare the analysis of variance table for these data. [12 Marks]
b) Test the null hypothesis that the population mean numbers of parts per batch not
conforming to standards are the same for all three suppliers at 5% level of

significance.

[8 Marks

Answer 1

Solution

We will solve ANOVA using Excel

So the output for anova from excel is given below

a) Prepare the analysis of variance table for these data.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Supplier A	6	192	32	11.2
Supplier B	6	146	24.33333	25.06667
Supplier C	6	209	34.83333	14.56667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	354.1111	2	177.0556	10.44918	0.001438	3.68232
Within Groups	254.1667	15	16.94444
Total	608.2778	17

b) Test the null hypothesis that the population mean numbers of parts per batch not
conforming to standards are the same for all three suppliers at 5% level of significance.

Here the F-statistic = 10.44918 >  F crit = 3.68232

So we reject the null hypothesis and conclude that population mean numbers of parts per batch not
conforming to standards are not same for all three suppliers at 5% level of significance.