https://file.aiquickdraw.com/mathbot/file/1729013531791yvx7xngh.jpg

The image you uploaded includes two tables and a request to calculate the chi-squared (χ²) statistic. Here's a breakdown of how we proceed:

### Step 1: Observed Values (from Table 1)
The observed frequency table is:

|                     | Companies with advertising budget < 200,000 USD | Companies with advertising budget >= 200,000 USD | Total |
|---------------------|-------------------------------------------------|--------------------------------------------------|-------|
| Companies with revenue >= 13M USD  | 4  | 13 | 17 |
| Companies with revenue < 13M USD   | 16 | 6  | 22 |
| **Total**            | 20  | 19 | 39 |

### Step 2: Expected Values (from Table 2)
The expected frequency table is:

|                     | Companies with advertising budget < 200,000 USD | Companies with advertising budget >= 200,000 USD | Total |
|---------------------|-------------------------------------------------|--------------------------------------------------|-------|
| Companies with revenue >= 13M USD  | 8.718 | 8.282 | 17 |
| Companies with revenue < 13M USD   | 11.282 | 10.717 | 22 |
| **Total**            | 20  | 19 | 39 |

### Step 3: Chi-Squared Formula
The formula for the chi-squared statistic is:

\[
\chi^2 = \sum \frac{(O - E)^2}{E}
\]

Where \(O\) represents the observed frequencies, and \(E\) represents the expected frequencies.

I'll calculate the chi-squared value now.The chi-squared (χ²) statistic calculated from the tables is approximately **9.29**.

If you need further details or would like to calculate the p-value or degrees of freedom, feel free to ask.

Here are some follow-up questions that might help you explore the problem further:

1. Would you like to calculate the p-value for this chi-squared test?
2. Should I explain how the degrees of freedom are determined in this case?
3. Are you interested in knowing how the chi-squared statistic is used to assess independence?
4. Do you want help interpreting this chi-squared result with a significance level (e.g., 0.05)?
5. Should I explain how the expected values were calculated in more detail?

**Tip**: The degrees of freedom for a chi-squared test in a contingency table is calculated as \((r-1)(c-1)\), where \(r\) is the number of rows and \(c\) is the number of columns.

Calculate chi-square (χ²) statistic based on observed and expected values in a contingency table.

This page explains how to calculate the chi-square (χ²) statistic based on observed and expected frequencies from a contingency table comparing companies' advertising budgets and revenues. The solution includes the chi-squared formula and details about its use in testing independence.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation