Section 10-3 – Comparing Two Variances The F-Distribution 2)F-distributions are positively skewed. 3)The total area under each curve of an F-distribution is equal to 1. 4)F-values are always greater than or equal to one. The larger variance is ALWAYS in the numerator!! 5)For all F-distributions, the mean value of F is approximately equal to 1.

Section 10-3 – Comparing Two Variances The F-Distribution Example 3 – Page 583 A restaurant manager is designing a system that is intended to decrease the variance of the time customers wait before their meals are served. Under the old system, a random sample of 10 customers had a variance of 400. Under the new system, a random sample of 21 customers had a variance of 256. At α = 0.10, is there enough evidence to convince the manager to switch to the new system? Assume both populations are normally distributed.

Section 10-3 – Comparing Two Variances The F-Distribution Example 3 – Page 583 To do this test on the TI-84, we go to STAT-TEST-E (2-SampFTest) Please be careful in entering the data!! The calculator asks for the standard deviation, not the variance. The standard deviation is the square root of the variance. We would enter the square root of 400 (20) for sample 1 We would enter the square root of 256 (16) for sample 2. Indicate whether it is a right, left, or two-tailed test. In this case, we have a right-tailed test. Calculate.

Section 10-3 – Comparing Two Variances The F-Distribution Example 4 – Page 584 You want to purchase stock in a company and are deciding between two different stocks. Because a stock’s risk can be associated with the standard deviation of its daily closing prices, you randomly select samples of the daily closing prices for each stock to obtain the results shown below. At α = 0.05, can you conclude that one of the two stocks is a riskier investment? Assume the stock closing prices are normally distributed. Stock AStock B

Assignments: Classwork:Page 585 #1-16 All Homework:Pages 585 – 586 #17-24 All