Question 1169148
To find the chi-square test statistic ($χ^2$) in this scenario, we use the following formula:

$χ^2 = \frac{(n-1)s^2}{σ_0^2}$

Where:

* $n$ = sample size
* $s$ = sample standard deviation
* $σ_0$ = population standard deviation (from the null hypothesis)

Here's how to break down the problem and find $χ^2$:

1.  **Gather the Information:**

    * $n = 20$ (sample size)
    * $σ_0 = 2.4$ inches (population standard deviation from the null hypothesis)
    * You need to calculate $s$ (sample standard deviation) from the table of player heights.

2.  **Calculate the Sample Standard Deviation (s):**

    * To do this, you'll need the player height data. You'll calculate the sample mean and then use that to calculate the sample standard deviation.
    * If you provide the data, I can calculate this for you.
    * The formula for sample standard deviation is:

        $s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$

        Where:

        * $x_i$ = each individual height
        * $\bar{x}$ = the sample mean
        * $n$ = sample size

3.  **Calculate the Chi-Square Test Statistic:**

    * Once you have the sample standard deviation ($s$), plug the values into the chi-square formula:

        $χ^2 = \frac{(20-1)s^2}{(2.4)^2}$
        $χ^2 = \frac{19s^2}{5.76}$

**Important Considerations:**

* **Data Entry:** The most crucial step is to accurately enter the player height data to calculate the sample standard deviation.
* **Hypothesis Test:** Remember that this chi-square value is a test statistic. To make a conclusion about the baseball analyst's claim, you would compare this calculated $χ^2$ value to a critical chi-square value from a chi-square distribution table. You'd use the appropriate degrees of freedom ($n-1 = 19$) and the significance level (alpha) you've chosen for the test.

**In summary:** To give you the exact $χ^2$ value, I need the height data from the table. If you provide that, I can walk you through the calculations.