Two independent samples are drawn from two normal populations, where the population variances are assumed to be equal. The sampling distribution of the ratio of the two sample variances is:
Question
Two independent samples are drawn from two normal populations, where the population variances are assumed to be equal. The sampling distribution of the ratio of the two sample variances is:
Solution
The question is asking about the sampling distribution of the ratio of two sample variances from two normal populations where the population variances are assumed to be equal.
Here are the steps to answer this question:
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Understand the concept: When two independent samples are drawn from two normal populations with equal variances, the ratio of the two sample variances follows a specific distribution.
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Identify the distribution: The ratio of two sample variances from two independent normal distributions follows an F-distribution.
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Understand the F-distribution: The F-distribution is a probability distribution that is used most commonly in Analysis of Variance (ANOVA). In this context, it is used to test hypotheses about the variances of two normal populations.
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Formulate the answer: Therefore, the sampling distribution of the ratio of the two sample variances is an F-distribution.
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