Question

A production manager was testing three different methods of production. Each method was assigned to a randomly selected set of workers (five each), and their time for the task completion was recorded (given below). The observations are independent, each population has the same variance, and are Normally distributed.

Method A	Method B	Method C
58	58	48
64	69	57
55	71	59
66	64	47
67	68	49

a) For this data, what is the value of the total sum of squares (i.e. sum of squares of deviations from the overall sample mean)?

b) For this data, what is the sum of squares within groups (also known as error sum of squares)?

c) We need to conduct an ANOVA test with the following hypotheses:

H0: the three population means are equal

H1: the three population means are not all equal

Test at 5% level of significance.

For this data, what is the F-statistic ( = MSwithin / MSbetween, also written as MSerror/MScolumns; here MS stands for mean square)? (Provide two decimal places)

d) For this test, what is the F critical value? (Provide two decimal places)

(You may copy the data and use Excel or StatCrunch to compute the result)

e) What is the conclusion of this test?

		population means are equal (i. e. we have no evidence against it)
		sample means are equal (i. e. we have no evidence against it)
		sample means are not all equal
		population means are not all equal

Answer 1

Excel Output:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Method A	5	310	62	27.5
Method B	5	330	66	26.5
Method C	5	260	52	31
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	520	2	260	9.176471	0.003818	3.885294
Within Groups	340	12	28.33333
Total	860	14

a) The value of the total sum of squares=SST=860

b) The sum of squares within groups=SSW=340

c) Value of F-statistic=9.18

d) Critical value=F_0.05,2,12=3.89

e) Since value of F-statistic>Critical value,

Option: population means are not all equal.