Complete the following steps. Identify each step with the appropriate corresponding number. 1. Write the claim and the null and the alternate hypotheses. 2. Identify a. 3. Draw a distribution to represent it and identify the critical value(s). 4. Write the inequality that identifies the rejection area(s). 5. Find the test statistic, p-value, and the correlation coefficient. 6. Make a decision about your test. 7. Write a sentence describing your decision about the claim in context with the problem. 1. Is there a relationship at a = 0.01 between muggings in a park in the city of Boston in the recent summer months and the number of police officers on duty in the park? A police cadet took a sample of the last 11 days and compiled the following data: x represents the number of police officers on duty in the park y represents the number of reported muggings that day 15 16 19 4 6 2 1 9 7 8 X Y 10 3 18 1 12 4 14 12 7 6 3 69

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**Instructions for Hypothesis Testing**

Complete the following steps. Identify each step with the appropriate corresponding number.

1. **Write the Claim and Hypotheses**
   - Identify the null and alternative hypotheses.

2. **Identify α**
   - Determine the significance level, which is given as α = 0.01.

3. **Draw a Distribution**
   - Represent the data distribution and identify the critical value(s).

4. **Write the Inequality**
   - Establish the inequality that represents the rejection area(s).

5. **Calculate Statistical Values**
   - Find the test statistic, p-value, and the correlation coefficient.

6. **Make a Decision**
   - Decide whether to reject or not reject the null hypothesis based on the statistical analysis.

7. **Contextualize the Decision**
   - Write a sentence describing the decision about the claim in the context of the problem.

---

**Research Problem:** 

Is there a relationship at α = 0.01 between muggings in a park in the city of Boston during recent summer months and the number of police officers on duty in the park? 

A police cadet recorded a sample from the last 11 days with the following data:

- **x**: Number of police officers on duty in the park
- **y**: Number of reported muggings that day

---

**Data Table:**

\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 10 & 15 & 16 & 19 & 4 & 6 & 18 & 12 & 14 & 7 & 3 \\
\hline
y & 3 & 2 & 1 & 1 & 9 & 7 & 8 & 1 & 4 & 2 & 6 \\
\hline
\end{array}
\]

- **x** represents the number of police officers on duty.
- **y** represents the number of reported muggings.
Transcribed Image Text:**Instructions for Hypothesis Testing** Complete the following steps. Identify each step with the appropriate corresponding number. 1. **Write the Claim and Hypotheses** - Identify the null and alternative hypotheses. 2. **Identify α** - Determine the significance level, which is given as α = 0.01. 3. **Draw a Distribution** - Represent the data distribution and identify the critical value(s). 4. **Write the Inequality** - Establish the inequality that represents the rejection area(s). 5. **Calculate Statistical Values** - Find the test statistic, p-value, and the correlation coefficient. 6. **Make a Decision** - Decide whether to reject or not reject the null hypothesis based on the statistical analysis. 7. **Contextualize the Decision** - Write a sentence describing the decision about the claim in the context of the problem. --- **Research Problem:** Is there a relationship at α = 0.01 between muggings in a park in the city of Boston during recent summer months and the number of police officers on duty in the park? A police cadet recorded a sample from the last 11 days with the following data: - **x**: Number of police officers on duty in the park - **y**: Number of reported muggings that day --- **Data Table:** \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 10 & 15 & 16 & 19 & 4 & 6 & 18 & 12 & 14 & 7 & 3 \\ \hline y & 3 & 2 & 1 & 1 & 9 & 7 & 8 & 1 & 4 & 2 & 6 \\ \hline \end{array} \] - **x** represents the number of police officers on duty. - **y** represents the number of reported muggings.
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