Review of Inference for Means

1. Review of Inference for Means Chapter 9

2. I can perform inference using a confidence interval or a significance test for a mean or difference in means or matched pairs situation. • I consistently calculate confidence intervals and test statistics correctly, showing formula, substitutions, correct critical values, and correct margins of error. • I consistently include all necessary steps in a confidence interval or significance test, including a check of conditions, hypotheses (for a test), and a conclusion or interpretation in context. • I consistently and correctly explain what the confidence interval or p-value means in the context of the problem. • I consistently and correctly interpret the meaning of 95% confidence in the context of the problem.

3. I can explain why we use t instead of z when doing inference for means. • I demonstrate an understanding that the capture rate for a confidence interval is less than advertised when the the population standard deviation s is estimated by the sample standard deviation s, unless adjusted by using t instead of z. • I demonstrate an understanding that the t statistic is different from the z statistic, and that this is due to using s to estimate s.

4. I can explain the link between the design of an experiment or sampling process and the inference procedure used to analyze the results. • I can explain how a difference in means for two independent samples differs from a matched pairs difference, both in the design and in the interpretation of the results.

5. One mean (confidence interval)Could also be asked alternatively to do a significance test • A simple random sample of 75 male adults living in a particular suburb was taken to study the amount of time they spent per week doing rigorous exercise. It indicated a mean of 73 minutes with a standard deviation of 21 minutes. Find the 95% confidence interval of the mean for all males in the suburb. Interpret this interval in words.

6. T vs. z The gas mileage for a certain model of car is known to have a standard deviation of 5 mi/gal. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gal. Construct a 95% confidence interval for the mean gas mileage for this car. Interpret the interval in words.

7. Difference of means (in an experiment) significance testCould also be asked alternatively to do a confidence interval The president of an all-female school stated in an interview that she was sure that students at her school studied more on average that the students at a neighboring all-male school. The president of the all-male school responded that he thought the mean student time for each student body was undoubtedly the same and suggested that a study be taken to clear up the controversy. Accordingly, independent samples were taken at the two schools with the following results. Determine at the 2% significance level if there is a significant difference between the mean study times of the students in the two schools.

8. Repeated measures/matched pairs significance testCould also be asked to do a confidence interval Six cars are selected randomly, equipped with one tire of brand A and one tire of brand B (the other two tires are not part of the test), and driven for a month. The amount of wear (in thousandths of an inch) is listed in the table below. At the = 0.05 level test the claim that the tire wear is the same.

9. Other big concepts from Chapter 9 • 15/40 rule • Ways to increase power? • Comparison of t and z distributions • When data isn’t normal • When do you pool with means?

10. For each problem things you should be asking yourself • Are they asking for a confidence interval or significance test? • Do I have one or two samples? • Do I know anything about the population SD? • If you do… well that’s z. If you don’t that’s t. • If I have two samples are they independent? • If yes, mean1- mean 2. • If no, look at the difference of means and go back to “one sample” of all their differences