Finding a Critical F-Value for a Right-Tailed Test In Exercises 5–8, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.


α=0.10, d.f.N=10, d.f.D=15

Verified step by step guidance

1. Identify the parameters for the F-distribution: the level of significance (α = 0.10), the degrees of freedom for the numerator (d.f.N = 10), and the degrees of freedom for the denominator (d.f.D = 15).
2. Understand that this is a right-tailed test, so the critical F-value corresponds to the point in the F-distribution where the area to the right equals the level of significance (α = 0.10).
3. Use an F-distribution table or statistical software to locate the critical F-value. In the table, find the row corresponding to d.f.N = 10 and the column corresponding to d.f.D = 15 under the α = 0.10 column.
4. If using statistical software (e.g., R, Python, or a calculator), input the parameters into the appropriate function for the F-distribution. For example, in R, you can use the function `qf(1 - α, d.f.N, d.f.D)` to find the critical F-value.
5. Record the critical F-value obtained from the table or software. This value will be used as the threshold for determining whether to reject the null hypothesis in the right-tailed test.

Key Concepts

F-Distribution

The F-distribution is a probability distribution that arises frequently in statistics, particularly in the context of variance analysis. It is used to compare the variances of two populations and is defined by two sets of degrees of freedom: one for the numerator and one for the denominator. The shape of the F-distribution is right-skewed, meaning it has a long tail on the right side, which is important for hypothesis testing in ANOVA and regression analysis.

Critical Value

A critical value is a threshold that determines the boundary for rejecting the null hypothesis in hypothesis testing. It is derived from the chosen level of significance (α), which represents the probability of making a Type I error. In a right-tailed test, the critical value is the point beyond which the test statistic is considered significant, indicating that the observed data is unlikely under the null hypothesis.

Degrees of Freedom

Degrees of freedom (d.f.) refer to the number of independent values or quantities that can vary in a statistical calculation. In the context of the F-test, there are two types of degrees of freedom: d.f.N (numerator) and d.f.D (denominator), which correspond to the number of groups being compared and the total number of observations, respectively. These values are crucial for determining the critical F-value from the F-distribution table.