Chapter 10 Inference on Two Samples 10.4 Inference on Two Population Standard Deviations

Requirements for Testing Claims Regarding Two Population Standard Deviations 1. The samples are independent simple random samples.

Requirements for Testing Claims Regarding Two Population Standard Deviations 1. The samples are independent simple random samples. 2. The populations from which the samples are drawn are normally distributed.

Fisher's F-distribution

Characteristics of the F-distribution 1. It is not symmetric. The F-distribution is skewed right.

Characteristics of the F-distribution 1. It is not symmetric. The F-distribution is skewed right. 2. The shape of the F-distribution depends upon the degrees of freedom in the numerator and denominator. This is similar to the distribution and Student’s t-distribution, whose shape depends upon their degrees of freedom.

Characteristics of the F-distribution 1. It is not symmetric. The F-distribution is skewed right. 2. The shape of the F-distribution depends upon the degrees of freedom in the numerator and denominator. This is similar to the distribution and Student’s t-distribution, whose shape depends upon their degrees of freedom. 3. The total area under the curve is 1.

Characteristics of the F-distribution 1. It is not symmetric. The F-distribution is skewed right. 2. The shape of the F-distribution depends upon the degrees of freedom in the numerator and denominator. This is similar to the distribution and Student’s t-distribution, whose shape depends upon their degrees of freedom. 3. The total area under the curve is The values of F are always greater than or equal to zero.

Is the critical F with n 1 – 1 degrees of freedom in the numerator and n 2 – 1 degrees of freedom in the denominator and an area of  to the right of the critical F.

To find the critical F with an area of α to the left, use the following:

EXAMPLE Finding Critical F values Find the critical F-value (a) for a right-tailed test with  = 0.1, degrees of freedom in the numerator = 8 and degrees of freedom in the denominator = 4. (b) for a two-tailed test with  = 0.05, degrees of freedom in the numerator = 20 and degrees of freedom in the denominator = 15.

Hypothesis Test Regarding the Two Means Population Standard Deviations