For a recent year, the following are the numbers of homicides that occurred each month in a city. Use a 0.05 significance level to test the claim that homicides in a 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? Full data set O Month Number Month Number Jan. 38 July Aug. Sep. Oc. Nov. 47 Feb. 31 50 March April May 46 50 39 43 45 38 June 48 Dec 38 Determine the null and alternative hypotheses. Calculate the test statistic, x. x2 = (Round to three decimal places as needed.) Calculate the P-value. P-value = (Round to four decimal places as needed.) %3D What is the conclusion for this hypothesis test? O A. Reject Ho. There is insufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months. O B. Reject Ho. There is sufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months. O C. Fail to reiect Ha. There is sufficient evidence to warrant reiection of the claim that homicides in a citv are eaually likelv for each of the 12 months. Click to select your answer(s).
For a recent year, the following are the numbers of homicides that occurred each month in a city. Use a 0.05 significance level to test the claim that homicides in a 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? Full data set O Month Number Month Number Jan. 38 July Aug. Sep. Oc. Nov. 47 Feb. 31 50 March April May 46 50 39 43 45 38 June 48 Dec 38 Determine the null and alternative hypotheses. Calculate the test statistic, x. x2 = (Round to three decimal places as needed.) Calculate the P-value. P-value = (Round to four decimal places as needed.) %3D What is the conclusion for this hypothesis test? O A. Reject Ho. There is insufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months. O B. Reject Ho. There is sufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months. O C. Fail to reiect Ha. There is sufficient evidence to warrant reiection of the claim that homicides in a citv are eaually likelv for each of the 12 months. Click to select your answer(s).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Hypothesis Testing for Monthly Homicide Rates**
For a recent year, the table below shows the number of homicides each month in a city. You are asked to use a 0.05 significance level to assess the hypothesis that homicides are equally likely each month. The question is whether there's evidence supporting the police commissioner's claim that more homicides occur in summer months due to better weather conditions.
| Month | Number | Month | Number |
|-------|--------|-------|--------|
| Jan. | 38 | July | 47 |
| Feb. | 31 | Aug. | 50 |
| March | 46 | Sep. | 50 |
| April | 39 | Oct. | 43 |
| May | 45 | Nov. | 38 |
| June | 48 | Dec. | 38 |
**Null and Alternative Hypotheses**
- \( H_0 \): Homicides are equally likely each month.
- \( H_1 \): Homicides are not equally likely each month.
**Calculate the Chi-Square Test Statistic (\( \chi^2 \))**
\[ \chi^2 = \text{(Use the data above and round to three decimal places as needed.)} \]
**Calculate the P-Value**
\[ \text{P-value} = \text{(Round to four decimal places as needed.)} \]
**Conclusion for the Hypothesis Test**
- **A.** Reject \( H_0 \): There is insufficient evidence to reject the claim of equal likelihood.
- **B.** Reject \( H_0 \): There is sufficient evidence to reject the claim of equal likelihood.
- **C.** Fail to reject \( H_0 \): There is sufficient evidence to warrant the claim of equal likelihood.
*Select the appropriate conclusion based on your calculations.*
This exercise helps understand the process of hypothesis testing and application of the chi-square test in real-world contexts, such as analyzing trends in crime data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8172651-744a-47c0-866b-aed0e3071054%2F647b6b01-b386-4f9d-a5f5-7e7337408ca4%2F3b7d9m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing for Monthly Homicide Rates**
For a recent year, the table below shows the number of homicides each month in a city. You are asked to use a 0.05 significance level to assess the hypothesis that homicides are equally likely each month. The question is whether there's evidence supporting the police commissioner's claim that more homicides occur in summer months due to better weather conditions.
| Month | Number | Month | Number |
|-------|--------|-------|--------|
| Jan. | 38 | July | 47 |
| Feb. | 31 | Aug. | 50 |
| March | 46 | Sep. | 50 |
| April | 39 | Oct. | 43 |
| May | 45 | Nov. | 38 |
| June | 48 | Dec. | 38 |
**Null and Alternative Hypotheses**
- \( H_0 \): Homicides are equally likely each month.
- \( H_1 \): Homicides are not equally likely each month.
**Calculate the Chi-Square Test Statistic (\( \chi^2 \))**
\[ \chi^2 = \text{(Use the data above and round to three decimal places as needed.)} \]
**Calculate the P-Value**
\[ \text{P-value} = \text{(Round to four decimal places as needed.)} \]
**Conclusion for the Hypothesis Test**
- **A.** Reject \( H_0 \): There is insufficient evidence to reject the claim of equal likelihood.
- **B.** Reject \( H_0 \): There is sufficient evidence to reject the claim of equal likelihood.
- **C.** Fail to reject \( H_0 \): There is sufficient evidence to warrant the claim of equal likelihood.
*Select the appropriate conclusion based on your calculations.*
This exercise helps understand the process of hypothesis testing and application of the chi-square test in real-world contexts, such as analyzing trends in crime data.
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