Presentation on theme: " I consistently calculate confidence intervals and test statistics correctly, showing formula, substitutions, correct critical values, and correct margins."— Presentation transcript:
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.
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.
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.
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.
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.
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
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
15/40 rule Ways to increase power? Comparison of t and z distributions When data isn’t normal When do you pool with means?
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