To determine the test statistic from the image, I'll need to analyze the content of the text and the table you've provided. The test statistic is usually calculated based on the data provided in the context of a hypothesis test. This involves understanding the hypothesis, the data presented, and the specific statistical test being applied.

I'll start by transcribing the key parts of the image:

1. **Text:** It likely describes the context, the hypothesis, or the method being used.
2. **Table:** Contains the data or results that are essential for calculating the test statistic.

Let's break it down:

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### **Textual Context:**
This part usually explains the nature of the test (e.g., a t-test, z-test, chi-square test, etc.), the hypothesis being tested, and the conditions or assumptions of the test. 

### **Table:**
This likely provides the observed data, expected data, or results from which the test statistic can be calculated.

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To accurately identify or calculate the test statistic, I would need to:

- Identify the type of test (e.g., t-test, chi-square, etc.).
- Determine whether the test is one-tailed or two-tailed.
- Examine the table to see if it provides values like the mean, standard deviation, or frequency counts.

### Steps to Calculate the Test Statistic:

1. **Identify the Hypothesis:**
   - Null hypothesis (\(H_0\)): Typically, it states that there is no effect or difference.
   - Alternative hypothesis (\(H_1\)): It states that there is an effect or difference.

2. **Select the Appropriate Test:**
   - This depends on the type of data and hypothesis. Common tests include t-tests, z-tests, chi-square tests, ANOVA, etc.

3. **Use the Formula:**
   - For a **t-test**: \( t = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}} \)
   - For a **z-test**: \( z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} \)
   - For a **chi-square test**: \( \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \)

4. **Calculate Using the Provided Data:**
   - Extract values from the table, such as means, standard deviations, sample sizes, observed and expected frequencies.

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If you could specify the type of test or provide additional details from the text or table, I can guide you through the precise calculation of the test statistic. If you'd like, I can extract specific numbers from the table for you.

Explore how to calculate the test statistic in hypothesis testing scenarios. Learn the formulas for t-tests, z-tests, and chi-square tests, and understand how to apply them using provided data. This guide covers essential statistical concepts and is suitable for advanced learners.

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