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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.

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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.

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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.

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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.

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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.

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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. SchoolSample SizeMean Study time (hrs) Standard Deviation (hrs) All Female6511.564.35 All Male7517.954.87

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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. Car123456 Brand A 12564943890106 Brand B 1336510337102115

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15/40 rule Ways to increase power? Comparison of t and z distributions When data isn’t normal When do you pool with means?

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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

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1 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 11 Comparing Two Populations or Treatments.

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