A sales organization conducted a study to explore sales​ strategies, processes, and support systems within businesses. Organizations were categorized by sales performance level​ (top performers vs. middle performers vs. bottom​ performers) and extent to which the organization invests in customer satisfaction. Results were organized into the accompanying contingency table. At the 0.01 level of​ significance, is there evidence of a significant relationship between sales performance level and level of investment in customer​ satisfaction? 	Top	Middle	Bottom
Annually	59	303	43
Every 2 to 4 years	35	232	22
Never	9	155	28. Calculate the test statistic.
chi Subscript STAT Superscript 2equals
  
enter your response here 
​(Round to two decimal places as​ needed.)
Part 3


To determine if there is a significant relationship between sales performance level and level of investment in customer satisfaction, we will use the **Chi-Square Test of Independence**. This test compares the observed frequencies to the expected frequencies under the assumption that the two variables (sales performance level and investment in customer satisfaction) are independent.

### Steps to calculate the test statistic:

1. **Observed Frequencies**: These are the values given in the contingency table:

| Investment in Customer Satisfaction | Top Performers | Middle Performers | Bottom Performers | Row Totals |
|-------------------------------------|----------------|-------------------|------------------|------------|
| Annually                            | 59             | 303               | 43               | 405        |
| Every 2 to 4 years                  | 35             | 232               | 22               | 289        |
| Never                               | 9              | 155               | 28               | 192        |
| **Column Totals**                   | 103            | 690               | 93               | 886        |

2. **Expected Frequencies**: The expected frequency for each cell is calculated using the formula:

   \[
   E_{ij} = \frac{(\text{Row Total}_i \times \text{Column Total}_j)}{\text{Grand Total}}
   \]
   where \( E_{ij} \) is the expected frequency for the cell in the ith row and jth column.

3. **Chi-Square Statistic Formula**: The test statistic is calculated as:

   \[
   \chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}
   \]
   where \( O_{ij} \) is the observed frequency and \( E_{ij} \) is the expected frequency.

Let's compute these values.The calculated Chi-Square test statistic is approximately \( \chi^2 = 17.28 \).

Would you like further details on the next steps, or do you have any specific questions?

Here are 5 related questions to explore:
1. How do you calculate the degrees of freedom for the Chi-Square test?
2. What is the critical value for the Chi-Square test at the 0.01 significance level?
3. How do you interpret the Chi-Square test results?
4. Can the Chi-Square test be used for continuous data?
5. What are the assumptions of the Chi-Square test?

**Tip**: Always ensure that the expected frequencies in each cell are sufficiently large (generally at least 5) to apply the Chi-Square test reliably.

A sales organization conducted a study to explore sales​ strategies, processes, and support systems within businesses. Organizations were categorized by sales performance level​ (top performers vs. middle performers vs. bottom​ performers) and extent to which the organization invests in customer satisfaction. Results were organized into the accompanying contingency table. At the 0.01 level of​ significance, is there evidence of a significant relationship between sales performance level and level of investment in customer​ satisfaction?

Top | Middle | Bottom
--- | ------ | ------
Annually | 59 | 303 | 43
Every 2 to 4 years | 35 | 232 | 22
Never | 9 | 155 | 28

Calculate the test statistic.

Learn how to apply the Chi-Square Test of Independence to determine the relationship between sales performance and customer satisfaction investment. Explore a step-by-step breakdown of the contingency table, calculation of expected frequencies, and the Chi-Square test statistic. Suitable for students in undergraduate statistics or advanced high school courses.

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