Randomly selected deaths of motorcycle riders in a region of the northern hemisphere are summarized in the accompanying table. Use a 0.05 significance level to test the claim that such fatalities occur with equal frequency in the different months. How might the results be explained?

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## Analysis of Monthly Motorcycle Rider Fatality Data

### Introduction
The following data set represents a randomly selected set of motorcycle rider fatalities in a region of the northern hemisphere. The goal is to determine, using a 0.05 significance level, if these fatalities occur with equal frequency throughout the months. This analysis will provide insight into whether there are seasonal variations or other factors influencing the rate of fatalities.

### Monthly Data on Motorcycle Rider Fatalities

| Month    | Number of Fatalities |
|----------|----------------------|
| January  | 7                    |
| February | 10                   |
| March    | 13                   |
| April    | 18                   |
| May      | 19                   |
| June     | 27                   |
| July     | 25                   |
| August   | 27                   |
| September| 26                   |
| October  | 12                   |
| November | 9                    |
| December | 9                    |

### Hypothesis Testing
**Task: Use a 0.05 significance level to test the claim that such fatalities occur with equal frequency in the different months.**

#### Steps:
A. **Determine the null and alternative hypothesis.**
   - **Null Hypothesis (H0):** Motorcycle rider fatalities occur with equal frequency in different months.
   - **Alternative Hypothesis (H1):** Motorcycle rider fatalities do not occur with equal frequency in different months.

B. **Calculate the test statistic (χ²).**
   - The test statistic for this data is calculated using the Chi-Square (χ²) test for goodness of fit.

C. **Determine the P-value.**
   - After calculating the χ² value from the observed and expected frequencies, the P-value is determined. This can be found using statistical tables or software that provides Chi-Square distribution data.

D. **Determine the conclusion for the hypothesis test.**
   - Based on the P-value and the significance level of 0.05, conclude whether to accept or reject the null hypothesis.

### Graphical Representation
To better understand the data, create a bar graph with months on the x-axis and the number of fatalities on the y-axis. This visual representation helps to quickly identify any potential trends or anomalies within the data.

*Example Conclusion:*
If the P-value calculated is less than 0.05, reject the null hypothesis, indicating that motorcycle rider fatalities do not occur with equal frequency throughout the year.

**Sample Interpretation
Transcribed Image Text:## Analysis of Monthly Motorcycle Rider Fatality Data ### Introduction The following data set represents a randomly selected set of motorcycle rider fatalities in a region of the northern hemisphere. The goal is to determine, using a 0.05 significance level, if these fatalities occur with equal frequency throughout the months. This analysis will provide insight into whether there are seasonal variations or other factors influencing the rate of fatalities. ### Monthly Data on Motorcycle Rider Fatalities | Month | Number of Fatalities | |----------|----------------------| | January | 7 | | February | 10 | | March | 13 | | April | 18 | | May | 19 | | June | 27 | | July | 25 | | August | 27 | | September| 26 | | October | 12 | | November | 9 | | December | 9 | ### Hypothesis Testing **Task: Use a 0.05 significance level to test the claim that such fatalities occur with equal frequency in the different months.** #### Steps: A. **Determine the null and alternative hypothesis.** - **Null Hypothesis (H0):** Motorcycle rider fatalities occur with equal frequency in different months. - **Alternative Hypothesis (H1):** Motorcycle rider fatalities do not occur with equal frequency in different months. B. **Calculate the test statistic (χ²).** - The test statistic for this data is calculated using the Chi-Square (χ²) test for goodness of fit. C. **Determine the P-value.** - After calculating the χ² value from the observed and expected frequencies, the P-value is determined. This can be found using statistical tables or software that provides Chi-Square distribution data. D. **Determine the conclusion for the hypothesis test.** - Based on the P-value and the significance level of 0.05, conclude whether to accept or reject the null hypothesis. ### Graphical Representation To better understand the data, create a bar graph with months on the x-axis and the number of fatalities on the y-axis. This visual representation helps to quickly identify any potential trends or anomalies within the data. *Example Conclusion:* If the P-value calculated is less than 0.05, reject the null hypothesis, indicating that motorcycle rider fatalities do not occur with equal frequency throughout the year. **Sample Interpretation
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