Question

assume that Friday morning taxi cab rides have times with a standard deviation of 10.5 minutes. A cab driver records times of rides during a Friday afternoon time period and obtains these statistics: n=16, x=18.1 minutes, s=13.8 minutes. use a 0.01 significance level to task the claim that these Friday afternoon times have greater variation than the Friday morning times assume that the sample is a simple random sample selected from a normally distributed population.

Answer 1

To test claim of greater variation in Friday afternoon times vs Friday morning times, use F-test for equality of variances with a 0.01 significance level.

Step-by-step explanation:

To test the claim that the Friday afternoon times have greater variation than the Friday morning times, we can use the F-test for equality of variances. The null hypothesis is that the variances are equal, and the alternative hypothesis is that the Friday afternoon times have greater variation. With a 0.01 significance level, we calculate the test statistic as F = (s₂² / s₁²), where s₁ is the standard deviation for the Friday morning times and s₂ is the standard deviation for the Friday afternoon times. We compare this test statistic to the critical value from the F-distribution table with degrees of freedom (n₁-1, n₂-1) where n₁ is the sample size for the Friday morning times and n₂ is the sample size for the Friday afternoon times. If the calculated test statistic is greater than the critical value, we reject the null hypothesis and conclude that the Friday afternoon times have greater variation than the Friday morning times.