Question

Roberta wants to compare productivity, as measured by the number of customers served, among three workers. The number of customers served by each worker is shown below.

Edward	Cathy	Brad
55	66	55
59	76	51
66	67	46
60	71	48

1. Is there a difference in the number of customers served? The level of significance is 0.01. Show all the five steps of the hypothesis testing.

Answer 1

Here we have data:

Edward	Cathy	Brad
55	66	55
59	76	51
66	67	46
60	71	48

Here we are using excel for calculation:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
55	3	185	61.6667	14.3333
66	3	214	71.3333	20.3333
55	3	145	48.3333	6.3333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	800.2222	2	400.1111	29.2764	0.0008	10.9248
Within Groups	82	6	13.6667
Total	882.2222	8

Hypothesis:

H_o; μ₁ = μ₂ = μ₃

H_a; At least one mean is difference from others.

Test statistics:

F = 29.2764

P-value = 0.0008

Critical value:

F_c = 10.9248

Reject the null hypothesis

Here we have sufficient evidence to reject the null hypothesis , F-observed value (29.2764) is greater than F-critical value (10.9248) and p-value (0.0008) is less than alpha value (0.01).

We can say that there is a difference in the number of customers served.