A police department released the numbers of calls for the different days of the week during the month of October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this analysis? Day Sun Mon Tues Wed Thurs Fri Sat Frequency 160 200 223 247 171 214 233 Calculate the test statistic, . = (Round to three decimal places as needed.)

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identify the test statistic, p value, and identify whether it is "reject" or "fail to reject" using stat crunch. 

**Analysis of Weekly Police Report Call Frequencies**

A police department released the numbers of calls for the different days of the week during the month of October. The data are presented in the table below. We will use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. 

**Fundamental Question:**
*What is the fundamental error with this analysis?*

**Data Table:**
```
| Day        | Sun | Mon | Tues | Wed | Thurs | Fri | Sat |
|------------|-----|-----|------|-----|-------|-----|-----|
| Frequency  | 160 | 200 | 223  | 247 | 171   | 214 | 233 |
```

**Null Hypothesis \(H_0\):**
- All days have the same frequency of calls.

**Alternative Hypothesis \(H_1\):**
- At least one day has a different frequency of calls than the other days.

**Calculate the test statistic, \( \chi^2 \):**

\[ \chi^2 = \boxed{\hspace{50px}} \]
*(Round to three decimal places as needed.)* 

**Instructions for Calculation:**
1. Calculate the expected frequency for each day by averaging the total number of calls over the 7 days.
2. Use the formula for the Chi-square test statistic:

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Where \(O_i\) is the observed frequency, and \(E_i\) is the expected frequency.

3. Compare the calculated \( \chi^2 \) value with the critical value from the Chi-square distribution table at a 0.01 significance level with 6 degrees of freedom (number of categories - 1).

This analysis helps in determining if the distribution of calls is uniform across the days of the week or if there are significant differences.
Transcribed Image Text:**Analysis of Weekly Police Report Call Frequencies** A police department released the numbers of calls for the different days of the week during the month of October. The data are presented in the table below. We will use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. **Fundamental Question:** *What is the fundamental error with this analysis?* **Data Table:** ``` | Day | Sun | Mon | Tues | Wed | Thurs | Fri | Sat | |------------|-----|-----|------|-----|-------|-----|-----| | Frequency | 160 | 200 | 223 | 247 | 171 | 214 | 233 | ``` **Null Hypothesis \(H_0\):** - All days have the same frequency of calls. **Alternative Hypothesis \(H_1\):** - At least one day has a different frequency of calls than the other days. **Calculate the test statistic, \( \chi^2 \):** \[ \chi^2 = \boxed{\hspace{50px}} \] *(Round to three decimal places as needed.)* **Instructions for Calculation:** 1. Calculate the expected frequency for each day by averaging the total number of calls over the 7 days. 2. Use the formula for the Chi-square test statistic: \[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \] Where \(O_i\) is the observed frequency, and \(E_i\) is the expected frequency. 3. Compare the calculated \( \chi^2 \) value with the critical value from the Chi-square distribution table at a 0.01 significance level with 6 degrees of freedom (number of categories - 1). This analysis helps in determining if the distribution of calls is uniform across the days of the week or if there are significant differences.
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