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.

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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.

Answers

Answer:Each month is equally likelyStep-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 monthsSet Hypotheses asH0: All months are equally likelyHa: 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 truewe 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=11p value = 0.497Since p >0.05 our alpha we accept H0Each month is equally likely

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