Questions: Find the critical value for a left-tailed test using the F distribution with α=0.025, degrees of freedom in the numerator =20, and degrees of freedom in the denominator =50. A portion of the table of critical values of the F-distribution is provided. What is the critical value? (Round to two decimal places as needed.)

Find the critical value for a left-tailed test using the F distribution with α=0.025, degrees of freedom in the numerator =20, and degrees of freedom in the denominator =50. A portion of the table of critical values of the F-distribution is provided.

What is the critical value?

(Round to two decimal places as needed.)

Transcript text: Find the critical value for a left-tailed test using the $F$ distribution with $\alpha=0.025$, degrees of freedom in the numerator =20, and degrees of freedom in the denominator =50. A portion of the table of critical values of the F-distribution is provided. What is the critical value? $\square$ (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Identify the Tail of the Test

The test is left-tailed, indicating the direction in which the critical value lies in the F-distribution.

Step 2: Determine the Significance Level ($\alpha$)

The given significance level for the test is $\alpha = 0.025$.

Step 3: Find Degrees of Freedom

The degrees of freedom in the numerator (df1) is 20, and in the denominator (df2) is 50.

Step 4: Use the F-Distribution Table or Function

Using the F-distribution, the critical value for a left-tailed with $\alpha = 0.025$, df1 = 20, and df2 = 50 is found.

Step 5: Rounding

The critical value is rounded to 2 decimal places, resulting in 1.99.

Final Answer:

The critical value for the given parameters is 1.99.

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