Problem 9BSC

In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion.

NYC Homicides 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. Is there sufficient evidence to support the police commissioner’s claim that homicides occur more often in the summer when the weather is better?

Answer:

Step 1 of 2

The expected values for each category, Ei , could be determined. With these observed and expected numbers of cases, the hypotheses can be written as

H0 : O = E

H1 : O E

Use a 0.05 significance level

SL. No. |
O |
p = 1/12 |
E = np |
(O - E )2 |
(O - E)2/E |

1 |
38 |
1/12 = 0.083333 |
42.66667 |
21.77778 |
0.510417 |

2 |
30 |
0.083333 |
42.66667 |
160.4444 |
3.760417 |

3 |
46 |
0.083333 |
42.66667 |
11.11111 |
0.260417 |

4 |
40 |
0.083333 |
42.66667 |
7.111111 |
0.166667 |

5 |
46 |
0.083333 |
42.66667 |
11.11111 |
0.260417 |

6 |
49 |
0.083333 |
42.66667 |
40.11111 |
0.940104 |

7 |
47 |
0.083333 |
42.66667 |
18.77778 |
0.440104 |

8 |
50 |
0.083333 |
42.66667 |
53.77778 |
1.260417 |

9 |
50 |
0.083333 |
42.66667 |
53.77778 |
1.260417 |

10 |
42 |
0.083333 |
42.66667 |
0.444444 |
0.010417 |

11 |
37 |
0.083333 |
42.66667 |
32.11111 |
0.752604 |

12 |
37 |
0.083333 |
42.66667 |
32.11111 |
0.752604 |

Sum |
N = 512 |
1 |
512 |
442.6667 |
10.375 |

The first step in conducting the significance test is to compute the expected frequency for each outcome given that the null hypothesis is true. For example, the expected frequency of a "1" is 12 since the probability of a "1" coming up is 1/12 and there were a total of 512.

Expected frequency (E) = np

= (512)(1/12)