The test statistic for this hypothesis test is calculated using the chi-square formula for variance:

$\chi^2 = \frac{(n - 1) \cdot s^2}{\sigma^2}$

Where:

• $n = 21$ (sample size)
• $s = 50.6$ (sample standard deviation)
• $\sigma = 53$ (population standard deviation under $H_0$)

Step 1: Calculate $s^2$ and $\sigma^2$:

$s^2 = 50.6^2 = 2560.36$ $\sigma^2 = 53^2 = 2809$

Step 2: Plug values into the formula for the test statistic:

$\chi^2 = \frac{(21 - 1) \cdot 2560.36}{2809}$ $\chi^2 = \frac{20 \cdot 2560.36}{2809} = \frac{51207.2}{2809}$ $\chi^2 \approx 18.23$

So, the test statistic is approximately 18.23.

Would you like to see the next steps or have any questions?

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Here are 5 related questions for practice:

1. How do you find the critical value for a chi-square test?
2. How would the test statistic change if the sample standard deviation were higher than 53?
3. What is the degree of freedom in this test?
4. How do you interpret the result of a chi-square test?
5. Can a chi-square test be used for non-normally distributed data?

Tip: The degrees of freedom in chi-square tests for variance are always $n-1$.