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

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level What is the p-value?

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Key Concepts

P-Value

The p-value is the probability, under the assumption that the null hypothesis is true, of obtaining a test statistic as extreme or more extreme than the one observed. It quantifies the evidence against the null hypothesis; a smaller p-value indicates stronger evidence in favor of the alternative hypothesis.

Significance Level

The significance level (often denoted as ?) is a threshold chosen by the researcher (for example, 10%) that determines when to reject the null hypothesis. If the p-value is less than or equal to this level, the null hypothesis is rejected, suggesting that the observed effect is statistically significant.

F-Test for Equality of Variances

The F-test is a statistical test used to compare two population variances by taking the ratio of the two sample variances. Under the null hypothesis of equal variances, this ratio follows an F-distribution with degrees of freedom determined by the sample sizes minus one for each sample.

Hypothesis Testing

Hypothesis testing is a statistical approach used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. It involves setting up a null hypothesis and an alternative hypothesis, and making decisions based on the likelihood (p?value) of the observed data if the null hypothesis were true.

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