Question

A small businessman is planning on opening a new retail location. Three locations are available, and he is interested in the annual income of families near each location. A random sample of 4 families is selected near each location, and the results are shown below (in thousands of dollars). Use this data to test the hypothesis that mean income is the same in all three areas.

Location 1	Location 2	Location 3
66	65	71
65	69	72
66	63	62
64	70	78

a) What is the critical value at the 0.01 significance level?

For full marks your answer should be accurate to at least two decimal places.

Critical value: 0

b) What is the F statistic?

For full marks your answer should be accurate to at least two decimal places.

F statistic: 0

c)

Can we conclude there is a difference in mean annual income? Yes, because the F statistic is greater than the critical value Yes, because the F statistic is less than the critical value No, because the F statistic is greater than the critical value No, because the F statistic is less than the critical value

Answer 1

procedure:
data -> data analysis -> anova: single factor

output:

analysis:
1)
critical value = F(0.01, 2, 9) = 8.021

2)
test statistic,
F = MSR/MSW = 64.67/166.25 = 1.75

3)
Null hypothesis, ho: there is no difference in the mean annual income between Location 1, 2 and 3.
The alternative hypothesis, h1: at least one of the mean annual income between Location 1, 2 and 3 differ significantly.
Since F < F(0.01, 2, 9), I fail to reject the null hypothesis and conclude that there is no difference in the mean annual income between Location 1, 2 and 3.

hence correct option is "No, because the F statistic is less than the critical value"