Question

A researcher is interested in whether the weather affects the number of muggings that occur in a city park. To study this question, he records the number of muggings that are reported to the police in a city park on three extremely hot summer days, three warm spring days, and on three cold winter days.

Cold day	Warm Day	Hot Day
2	4	5
2	4	6
3	3	4

What is the null and the research hypotheses? Calculate the F ratio.   Are your results statistically significant, and if so, at what level? What are your conclusions about the null hypothesis?

Answer 1

Null hypothesis H, : = t = Alternative hypothesis H, : At least one of the means is different from the others. From the given information, N = 9, Grand total G=x = 33, Raw sum of squares = {x* = 135, (33) correction factor (CF) = =121, N N 9 = = SaS = x - =135-121 =14, N ((7)(11) (15) SS, Between SST = Σ + + - 121 =10.67, N 3 3 3 - SS. within SISE SS SST = 14-10.67 = 3.33. Total ANOVA table Source DF SS MS F P-value 10.67 5.33 Between groups 3-1= 2 10.67 =5.33 -=9.52 0.013 2 0.56 3.33 Within groups( Error) 9-3 = 6 3.33 = 0.56 6 Total 9-1 = 8 14.00 The critical value is F(2,6)= 5.14 at 0.05 level of significance. The value of the test statistic F = 9.52 greater than the critical value F(2,6)= 5.14, we reject the null hypothesis. P-value = 0.013 less than the level of significance a = 0.05, Reject the null hypothesis. There is enough evidence to conclude that the weather affects the number of muggings that occur in a city park.