Question

Consider the results from a completely randomized design showing commuting times in three states. Use an appropriate Excel ANOVA tool, to test for any significant differences in commuting times between the three states. Use α = 0.05.

Illinois	Ohio	Texas
26.8	27.5	10.1
17.6	28.9	18.8
27	19.1	31.4
20	36.9	44.2
50.7	40.8	24.6
24.4	9.5	29.5
36.8	37.4	38.1
42.2	38.9	30.3
26.3	46.2	11.7
14	35.8	35.8
28.5	20.7	22.4
36.9	37.8	17
25.6	49.7	15.4
25.9	44.3	15.4
29.5	12.1	6.8
29.7	43.7	14.8
30.5	35.9	59.3
20	30.2	5.3
23.2	8.5	0.6
20.7	34.6	20.7
6.2	37.9	18.6
44.2	50.9	24.9
28.2	24.2	9.3
28.8	39.1	11.9
16.6	20.4	19.6
20.2	12.4	31
13.1	28	25.9
16.9	28.4	52.6
32.4	19.4	38.3
19.6	42.5	34
12.8	27.2	24.9
30.2	22.6	32.1
65.1	50.8	43
25.5	34.1	31.1
17.5	27.1	16.8
11.1	38.9	34.1
48.8	28.7	40.4
38.9	54.2	29.4
23.1	30.6	9.8
21.6	15.9	19.5
22.3	15.1	9.6
27.3	30.1	21.6
30.7	32.2	26.5

Answer 1

Testing against at least one mean is different

Using Excel, (Data -> Data Analysis -> ANOVA : single factor), we get the following output -

Now,

The value of F statistic F = 3.57436

and p-value = 0.03091

Since p-value < 0.05, so we reject the null hypothesis at 5% level of significance and we can conclude that there is significant difference in commuting times between the three states.