Question

The federal government of Canada believes that the average response times of emergency response services vary too much across the country. To investigate this, the government obtained independent random samples of 10 response times from each of three large cities. In order to compare the mean response times for the three cities, the data were subjected to an analysis of variance. The results of the ANOVA are summarized in the table below. How would the p-value of the ANOVA F-test be interpreted with α = 0.01?

	Degree of freedom	Sqrt Sum	Mean Sqrt
SOURCE	Df	SS	MS	F
Group	2	0.467	0.234	0.636
Error	27	9.9	0.367
Total	29

Answer 1

From the given ANOVA table

Sources                 df                     SS                    MS                   F

Group                   2                      0.467               0.234               0.636

Error                      27                    9.9                   0.367

Total                     29

the value of F stat is 0.636

From F table , F at 0.01 with df ( 2,27) is 5.488

since F < 5.488 so option C is true

The mean response times differ significantly for the three cities at α=0.01

Answer 2

Thank you for the response!

I have calculated p=0.537153

Since the p-value is greater than alpha 0.01 then the null hypothesis is not rejected. The null hypothesis in this case is that the average response times vary significantly across the country.