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The question asks for the calculation of the F-statistic to test the null hypothesis that the variances of two independent populations are equal, i.e., \( H_0: \sigma_1^2 = \sigma_2^2 \).

The formula to compute the F-statistic for comparing two variances is:

\[
F = \frac{S_A^2}{S_B^2}
\]

Where:
- \( S_A^2 \) is the sample variance for Population A,
- \( S_B^2 \) is the sample variance for Population B.

From the given dataThe question asks for the calculation of the F-statistic to test the null hypothesis that the variances of two independent populations are equal, i.e., \( H_0: \sigma_1^2 = \sigma_2^2 \).

The formula to compute the F-statistic for comparing two variances is:

\[
F = \frac{S_A^2}{S_B^2}
\]

Where:
- \( S_A^2 \) is the sample variance for Population A,
- \( S_B^2 \) is the sample variance for Population B.

From the given 
- \( S_A^2 = 183.5 \)
- \( S_B^2 = 101.1 \)

Now, let’s compute the F-statistic.

\[
F = \frac{183.5}{101.1}
\] 

Let me calculate that for you.The value of the F-statistic is approximately 1.815 (rounded to four decimal places).

Would you like further details or have any additional questions?

Here are 5 related questions to expand on this concept:
1. How do you determine the critical value for the F-test?
2. What are the degrees of freedom for this F-test?
3. When would you reject the null hypothesis in an F-test?
4. How is the F-distribution different from other distributions, such as the normal or t-distribution?
5. Can the F-statistic ever be negative, and why?

**Tip:** When performing an F-test, always remember to check whether you are performing a one-tailed or two-tailed test, as this affects the critical value.

The following information is available for two samples drawn from independent normally distributed populations. Population A: n_A = 10, S_A^2 = 183.5. Population B: n_B = 10, S_B^2 = 101.1. What is the value of F if you are testing the null hypothesis H_0: σ_1^2 = σ_2^2?

Learn how to calculate the F-statistic for testing the null hypothesis H_0: σ_1^2 = σ_2^2 using sample data from two independent normally distributed populations. With sample variances S_A^2 = 183.5 and S_B^2 = 101.1, this guide provides a detailed step-by-step solution.

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