Multiple Choice
Two machines produce metal rods. You take independent random samples of their lengths (shown below) as part of a hypothesis test. Calculate the F statistic for this test.
Sample A:
Sample B:
10. Hypothesis Testing for Two Samples
Two Variances and F Distribution
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
In a two-sample Hypothesis Test for Variance, what does an -statistic near 1 indicate?
A
Both populations have zero variance.
B
We reject the null hypothesis .
C
The numerator variance is smaller than the denominator variance.
D
The two sample variances are approximately equal.
Verified step by step guidance1
Recall that in a two-sample hypothesis test for variance, the null hypothesis \(H_0\) typically states that the variances of the two populations are equal, i.e., \(\sigma_1^2 = \sigma_2^2\).
The test statistic used is the \(F\)-statistic, which is calculated as the ratio of the two sample variances: \(F = \frac{S_1^2}{S_2^2}\), where \(S_1^2\) and \(S_2^2\) are the sample variances from the two groups.
An \(F\)-statistic near 1 means that the numerator variance and the denominator variance are very close in value, indicating little difference between the two sample variances.
Since the \(F\)-statistic measures the ratio of variances, a value near 1 suggests that the evidence does not support rejecting the null hypothesis \(H_0\) that the population variances are equal.
Therefore, an \(F\)-statistic near 1 indicates that the two sample variances are approximately equal, consistent with the null hypothesis.
Related Videos
Related Practice
Two Variances and F Distribution practice set
Problem sets built by lead tutorsExpert video explanations