Use the following information to answer the next three...

Use the following information to answer the next three exercises. Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their variances are the same or different. State the null and alternative hypotheses.

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Key Concepts

Null Hypothesis

This is the default assumption in hypothesis testing which posits no effect or no difference. In a variance comparison, it states that the two groups have equal population variances. It serves as the benchmark against which any observed differences in sample variances are measured.

Alternative Hypothesis

This is the hypothesis that contradicts the null hypothesis, suggesting that there is a measurable difference between the groups. In the context of comparing variances, it asserts that the two population variances are not equal, which may indicate variability in the underlying processes of the groups.

F-Test for Equality of Variances

This is a statistical method used to compare the variances of two normally distributed populations. It involves calculating the ratio of the two sample variances, and if this ratio is significantly different from what is expected under the null hypothesis, it provides evidence to reject the null hypothesis in favor of the alternative.

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