EXAMS Mon. Tues. Wed. Thur. Fri. 5/7 (Odd) 5/8 (Even) 5/9 (Odd) Section 10-3 Section 10-4 5/14 (Even) 5/15 (Odd) 5/16 (Even) 5/17 5/18 Make-Up (Odd) Shortened Blocks 2, 4, 6 Extended Block 1 Extended Block 2 Extended Block 3 5/21 5/22 5/23 5/24 5/25 Extended Block 4 Extended Block 5 Extended Block 6 Extended Block 7 Reg. Sched. 5/28 5/29 (Even) 5/30 (Odd) 5/31 (Even) 6/1 (Odd) MEMORIAL DAY EXAMS

Section 10-3 – Comparing Two Variances The F-Distribution Let 𝑠 1 2 and 𝑠 2 2 represent the sample variances of two populations. If both populations are normal, and the population variances 𝜎 1 2 and 𝜎 2 2 are equal, then the sampling distribution of 𝐹= 𝑠 1 2 𝑠 2 2 is called an F-distribution. The populations must be independent and normally distributed. Guidelines for Using a Two-Sample F-Test to Compare 𝜎 1 2 and 𝜎 2 2 . 1) Write the hypotheses and identify the claim. 2) Identify α. 3) STAT-TEST-E. Make sure to enter the values correctly. The calculator asks for the sample standard deviations; if you are given the variances you will need to convert to standard deviations (take the square roots). 4) Make a decision to reject or fail to reject the null hypothesis.

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. Remember that the larger variance is the numerator, so 400 is 𝑠 1 2 , and 256 is 𝑠 2 2 . In other words, 𝑠 1 2 and σ 1 2 are the sample variance and the population variance of the old system. To write the hypotheses, we need to understand that the claim is that “the variance of waiting times under the new system is less than the variance of waiting times under the old system”, 𝑠 2 2 < 𝑠 1 2 H0: 𝑠 1 2 ≤𝑠 2 2 Ha: 𝑠 1 2 > 𝑠 2 2 (claim) This makes this a right-tailed test.

Section 10-3 – Comparing Two Variances The F-Distribution Example 3 – Page 583 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. Use 10 for n1. We would enter the square root of 256 (16) for sample 2. Use 21 for n2. Indicate whether it is a right, left, or two-tailed test. In this case, we have a right-tailed test. Calculate. If p ≤ α, reject H0. If p > α, fail to reject H0. In this case, p = .194, which is > .10, so we fail to reject 𝐻 0 . At the 10% confidence level, there is not enough evidence to convince the manager to switch systems.

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. Since 5.7 is greater than 3.5, 5.7 will be 𝑠 1 2 , and 3.5 will be 𝑠 2 2 . 𝑠 1 2 = 5.7 2 , 𝑠 2 2 = 3.5 2 (Stock B is represented by 𝑠 1 2 and 𝜎 1 2 .) Stock A Stock B 𝑛 2 =30 𝑛 1 =31 𝑠 2 =3.5 𝑠 1 =5.7

Section 10-3 – Comparing Two Variances The F-Distribution Example 4 – Page 584 To write the hypotheses, remember that the claim is that “one of these stocks is a riskier investment”. This means that the variances are not equal. 𝐻 0 : 𝑠 1 2 = 𝑠 2 2 𝐻 𝑎 : 𝑠 1 2 ≠ 𝑠 2 2 (claim) STAT-TEST-E (2-SampFTest) Since we were given the standard deviations in this problem, we enter them as given. Use 5.7 for Sx1 and 31 for n1. Use 3.5 for Sx2 and 30 for n2. Select two tailed test and Calculate. The test gives us the p-value of .0102, which we can compare to α. .0102 < .05, so we reject the null. At the 5% level of significance, there is enough evidence to conclude that one of these stocks is a riskier investment.

Classwork: Page 585 #3, 11-16 All Homework: Pages 585-586 #17-24 All (Skip part b)