A police chief wants to determine if crime rates are different for four differen

Question

A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South(4) sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below.

1) The competing hypotheses about the mean crime rates are

a) H0: 1 = 2 = 3, HA: Not all population means are equal

b) H0: 1 = 2 = 3 = 4, HA: Not all population means are equal

c) H0: Not all population means are equal, HA: 1 = 2 = 3

d)H0: Not all population means are equal, HA: 1 = 2 = 3 = 4

2) At the 1% significance level, the critical value is

a) 2.38

b) 3.86

c) 4.94

d) 3.10

3) At the 1% significance level, the conclusion for the hypothesis test is _______

a) do not reject the null hypothesis; we cannot conclude that not all mean numbers of crimes are equal

b) reject the null hypothesis; we cannot conclude that not all mean number of crimes are equal

c) do not reject the null hypothesis; not all mean number of crimes are equal

d) reject the null hypothesis; not all mean number of crimes are equal

Explanation / Answer

1) Hypothesis about mean crime rates are (option b)

H0: 1 = 2 = 3 = 4,

Ha: Not all population means are equal

2) At 1% level of significance critical value at (3, 20) degrees of freedom = 4.938 (C)

3) At 1 % level of significance, calculated value 9.12 is greater than F critical value 4.938 we reject null hypothesis

Hence concusion is

d) reject the null hypothesis; not all mean number of crimes are equal

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