### Analysis of Sales Proportion Across Multiple LocationsA store manager conducts an experiment to determine whether the proportion of sales for a specific item varies significantly across five different store locations. The manager monitors the number of items sold in each location over a week. The aim is to determine if there is a significant difference in the sales proportions using a significance level of $\alpha = 0.05$.The observed data is compiled, and students are required to complete the table by calculating the expected values and comparing them with the observed counts. The table also includes a column for the Chi-square statistic component, $\frac{(O - E)^2}{E}$.#### Step-by-Step Example:1. **Observed Sales (O):** The actual count of items sold in each location: - Location A: 22 items - Location B: 7 items - Location C: 8 items - Location D: 13 items - Location E: 24 items2. **Expected Sales (E):** Expected count if the sales proportions are the same across all locations. It is calculated using $\frac{\text{Total Number of Items Sold}}{\text{Number of Locations}}$. For this example: - Total items sold = 74 - Number of locations = 5 - Expected sales per location $E = \frac{74}{5} = 14.8$3. **Chi-Square Statistic $\frac{(O - E)^2}{E}$:** This measures the discrepancy between observed and expected counts. It is computed for each location.Let's fill out the table with this data:| Location | Observed (O) | Expected (E) | $\frac{(O - E)^2}{E}$ ||----------------|-----------------|-------------------|-------------------------------|| A | 22 | 14.8 | $\frac{(22 - 14.8)^2}{14.8}$ ≈ 3.4730|| B | 7 | 14.8 | $\frac{(7 - 14.8)^2}{14.8}$ ≈ 4.1054 || C | 8 | 14.8 | \(\frac{(8 - 14.8)^2}{14 ## Chi-Square Test Instructions### b. Calculate the Chi-Square Test-Statistic\[ \chi^2 = \]*Note: In this section, you should compute the chi-square (χ²) test statistic based on your observed and expected frequencies. Enter your calculated value in the provided space.*### c. Calculate the p-value\[ \text{p-value} = \]*Note: After obtaining the chi-square test statistic, use the chi-square distribution table or a statistical software to find the p-value. Enter the p-value in the provided space.*### d. This p-value leads to a decision to:*In this section, you will decide the conclusion based on the p-value calculated in part (c). Select the appropriate option:* - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null - [ ] accept the alternative### e. As such, the final conclusion is that:*Based on your decision in part (d), choose the correct interpretation of the results:* - [ ] There is sufficient evidence to support the claim that there is a difference in the proportion of items sold for the 5 store locations. - [ ] There is not sufficient evidence to support the claim that there is a difference in the proportion of items sold for the 5 store locations.*When interpreting the final conclusion, ensure that it aligns with the hypothesis you are testing and the results obtained from your calculations.*

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A store manager wants to see if the of sales for an store. The manager observes the number of items sold in each location for a week. Test to see if there is a difference or no difference in the proportions using a = 0.05 a. Complete the table. Round answers to least 4 decimal places. (0 – E) Location Observed Expected E A 22 B 7 C 8 13 24 Total 74

A store manager wants to see if the of sales for an store. The manager observes the number of items sold in each location for a week. Test to see if there is a difference or no difference in the proportions using a = 0.05 a. Complete the table. Round answers to least 4 decimal places. (0 – E) Location Observed Expected E A 22 B 7 C 8 13 24 Total 74

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### Analysis of Sales Proportion Across Multiple Locations

A store manager conducts an experiment to determine whether the proportion of sales for a specific item varies significantly across five different store locations. The manager monitors the number of items sold in each location over a week. The aim is to determine if there is a significant difference in the sales proportions using a significance level of $\alpha = 0.05$.

The observed data is compiled, and students are required to complete the table by calculating the expected values and comparing them with the observed counts. The table also includes a column for the Chi-square statistic component, $\frac{(O - E)^2}{E}$.

#### Step-by-Step Example:

1. **Observed Sales (O):**
The actual count of items sold in each location:
- Location A: 22 items
- Location B: 7 items
- Location C: 8 items
- Location D: 13 items
- Location E: 24 items

2. **Expected Sales (E):**
Expected count if the sales proportions are the same across all locations. It is calculated using $\frac{\text{Total Number of Items Sold}}{\text{Number of Locations}}$.

For this example:
- Total items sold = 74
- Number of locations = 5
- Expected sales per location $E = \frac{74}{5} = 14.8$

3. **Chi-Square Statistic $\frac{(O - E)^2}{E}$:**
This measures the discrepancy between observed and expected counts. It is computed for each location.

Let's fill out the table with this data:

| Location | Observed (O) | Expected (E) | $\frac{(O - E)^2}{E}$ |
|----------------|-----------------|-------------------|-------------------------------|
| A | 22 | 14.8 | $\frac{(22 - 14.8)^2}{14.8}$ ≈ 3.4730|
| B | 7 | 14.8 | $\frac{(7 - 14.8)^2}{14.8}$ ≈ 4.1054 |
| C | 8 | 14.8 | \(\frac{(8 - 14.8)^2}{14

## Chi-Square Test Instructions

### b. Calculate the Chi-Square Test-Statistic
\[ \chi^2 = \]
*Note: In this section, you should compute the chi-square (χ²) test statistic based on your observed and expected frequencies. Enter your calculated value in the provided space.*

### c. Calculate the p-value
\[ \text{p-value} = \]
*Note: After obtaining the chi-square test statistic, use the chi-square distribution table or a statistical software to find the p-value. Enter the p-value in the provided space.*

### d. This p-value leads to a decision to:
*In this section, you will decide the conclusion based on the p-value calculated in part (c). Select the appropriate option:*

- [ ] reject the null
- [ ] accept the null
- [ ] fail to reject the null
- [ ] accept the alternative

### e. As such, the final conclusion is that:
*Based on your decision in part (d), choose the correct interpretation of the results:*

- [ ] There is sufficient evidence to support the claim that there is a difference in the proportion of items sold for the 5 store locations.
- [ ] There is not sufficient evidence to support the claim that there is a difference in the proportion of items sold for the 5 store locations.

*When interpreting the final conclusion, ensure that it aligns with the hypothesis you are testing and the results obtained from your calculations.*

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