Question

For a recent​ year, the following are the numbers of homicides that occurred each month in New York​ City: 38,​ 30, 46,​ 40, 46,​ 49, 47,​ 50, 50,​ 42, 37, 37. Use a 0.05 significance level to test the claim that homicides in New York City are equally likely for each of the 12 months. State your conclusion about the claim.

Answer 1

Each month is equally likely

Explanation:

Given that for a recent​ year, the following are the numbers of homicides that occurred each month in New York​ City:

38,​ 30, 46,​ 40, 46,​ 49, 47,​ 50, 50,​ 42, 37, 37.

We have to check whether it is equally likely for each of the 12 months

Set Hypotheses as

H0: All months are equally likely

Ha: atleast two months are not equally likely

(Two tailed chisquare test at 5% significance level)

This is a test for chi square goodness of fit and so assuming H0 to be true

we divide the total equaly among 12 months as expected

Observed Expected Chi square

Jan 38 42.66666667 0.510416667

Feb 30 42.66666667 3.760416667

Mar 46 42.66666667 0.260416667

Apr 40 42.66666667 0.166666667

May 46 42.66666667 0.260416667

June 49 42.66666667 0.940104167

July 47 42.66666667 0.440104167

Aug 50 42.66666667 1.260416667

Sep 50 42.66666667 1.260416667

Oct 42 42.66666667 0.010416667

Nov 37 42.66666667 0.752604167

Dec 37 42.66666667 0.752604167

Total 512 512 10.375

df=11

p value = 0.497

Since p >0.05 our alpha we accept H0

Each month is equally likely