Question
When a researcher wants to test whether two samples can be regarded as drawn from the normal populations having same variance by using variance ratio, which one of the following tests of hypothesis is appropriate ?
The correct answer is
F-test
Identifying the Appropriate Variance Ratio Test
The question asks for the appropriate hypothesis test to determine if two samples, assumed to be from normal populations, have the same variance. This involves comparing the variances of these two populations.
Understanding Hypothesis Testing for Variances
When comparing the variances of two populations, the standard approach uses the ratio of their sample variances. The goal is to test the null hypothesis that the population variances are equal.
Appropriate Test: F-test
- The F-test is specifically designed to compare the variances of two populations.
- It utilizes the ratio of the sample variances ($s_1^2$ and $s_2^2$) from the two samples.
- The test statistic follows an F-distribution under the null hypothesis ($H_0: \sigma_1^2 = \sigma_2^2$).
- This directly addresses the question of whether the two samples can be regarded as having the same variance.
Why Other Tests Are Inappropriate
- Z-test: Primarily used for comparing means when population variance is known or for large sample sizes. Not suitable for comparing variances directly.
- t-test: Used for comparing means when population variance is unknown. It does not directly test for equality of variances.
- Chi-square test: Can be used to test if a *single* sample variance matches a hypothesized population variance, but it's not the standard test for comparing the variances of *two* samples using their ratio.
Therefore, the F-test is the correct choice for testing the equality of variances between two populations using the variance ratio.
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Important Questions from Hypothesis testing - Teaching
- Type II error occurs when :
- The null hypothesis in nonparametric test often _______.
1. Includes specification of a population's parameters
2. Is used to evaluate some general population aspect
3. Is very similar to that used in regression analysis
4. Simultaneously tests more than two population parameters - The _______ test determines whether there is a significant difference between the observed and hypothesized distribution for a sample.
1. Independence
2. Coefficient of determination
3. Correlation analysis
4. Goodness-of-fit - Match the LIST-I with LIST-II
LIST-I LIST-II A. One-Tailed Test I. Null hypothesis is rejected if the sample value is significantly higher or lower than the hypothesized value of the population parameter B. Paired difference Test II. A hypothesis test of the difference between the sample means of two independent samples C. Two-Tailed Test III. A sample value significantly above the hypothesized population value will lead to rejection of the null hypothesis D. Upper-Tailed Test IV. Concerned only with whether the observed value deviates from the hypothesized value in one direction
Choose the correct answer from the options given below: - The null hypothesis that all slope coefficients are simultaneously equal to zero is tested in logit model by:
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