1. Comparing Means Chapter 24

2. déjà vu’ this is our t-value; it works a lot like a z-score. You can use the InvT function in the calculator to get your p-value. With degrees of freedom calculated from a special formula

3. Special Degrees of Freedom Formula

4. Our Conditions 1.Independence 1.Is it randomized and less than 10% of the population? 2.Normal Population 1.Nearly Normal Condition 1.If n<15, histogram should show almost now skewness, and be unimodal 2.If n = 40 or close to it, should be mostly normal, moderate skewness can be tolerated. 3.Independent Groups 1.Are the two groups being tested independent of each other? You just have to think through this one.

5. A confidence interval.

6. Step by Step; two sample t-interval Brand NameGeneric 194190.7 205.5203.5 199.2203.5 172.4206.5 184.0222.5 169.5209.4 The data table below shows the lives of two batteries tested under identical experiment conditions (in minutes). Let’s make a confidence interval for the differences of means.

7. Plan Identify the parameter you wish to estimate, and the populations you want to make statements about. Make a picture Response

8. What model will we use? Model Check the appropriate assumptions and conditions. Response Independent Groups: Batteries manufactured by two different companies should be independent. Randomization: The batteries were involved in a experiment, meaning randomization should have been employed. Its also fair to assume that 6 batteries is less than 10% of the population of either brand. Nearly Normal: Check the histogram on page 552. Do you know how to make one in your calculator? The conditions are met for a Student’s t- model. We’ll use a two-sample t-interval.

9. Show Mechanics Show all of your calculations. We need to calculate several values here. 1.The standard error 2.Approximate degrees of freedom. 3.Critical t-value (from table) 4.Margin of Error. Response Use the calculator; 2 Sample T- interval. a.Input the data into List 1 and List 2 in the calculator. b.Use the 2-sample T interval function in the calculator (Stat>Test>0 2SampT-Int) c.Leave both Frequency options at 1, and select NO for pooled. d.Calculate

10. Show cont. Important Pieces 1.The interval. Your calculator will automatically use List1 – List 2. If that yields negative results, you must interpret them correctly. Response The calculator gave (-35.1, - 2.069). Since we used Generic – Brand, our answer will be (2.069, 35.1).

11. Tell Interpret your results both statistically and in the context of the problem. Response. The 95% confidence interval is (2.1, 35.1) minutes. I am 95% confident that hte interval from 2.1 minutes to 35.1 minutes captures the mean amount of time generic batteries outlast name brand batteries.

12. A test for difference between two means.

13. Example Refer to the example about cameras on pages 554-558 in your book for a hypothesis test.