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

Answer:

Each month is equally likely

Step-by-step 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