Chi-Square Test for Variance in Math

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Questions and Answers

What is the null hypothesis for the given sample chi-square test for variance?

The null hypothesis is that the standard deviation of the exam scores is 5 points.

What is the alternative hypothesis for the given sample chi-square test for variance?

The alternative hypothesis is that the standard deviation of the exam scores is more than 5 points.

What is the test statistic used in the sample chi-square test for variance?

The test statistic used is the sample variance, $(n-1)s^2/\sigma_0^2$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma_0^2$ is the hypothesized variance under the null hypothesis.

What is the p-value for the sample chi-square test for variance, given that the sample standard deviation is 8 points and the hypothesized standard deviation is 5 points?

<p>The p-value is the probability of observing a test statistic as extreme or more extreme than the calculated value, under the assumption that the null hypothesis is true.</p> Signup and view all the answers

Assuming a significance level of $\alpha=0.05$, what is the conclusion of the sample chi-square test for variance?

<p>If the p-value is less than the significance level of 0.05, we would reject the null hypothesis and conclude that the standard deviation is more than 5 points. Otherwise, we would fail to reject the null hypothesis.</p> Signup and view all the answers