1. Warm-up Day of 8.1 and 8.2 Review

5. 8.2 P#20, 23 and 24 P#20 a. and b. c. Since the p-hat is along the line for reasonably likely events.

7. 8.2 Type of Errors The logic of guilty or not guilty works when thinking about whether to reject or fail to reject the null hypothesis. When understanding errors in hypothesis testing, it is best to think of medical tests to determine if a disease is present.

8. Other ways to remember. Normally you start with the idea that the null hypothesis is true, and that the person is healthy. So your first mistake would be to reject the null hypothesis or to declare the person diseased. This would be your Type I error. When do Type I errors occur? They occur when you have the bad luck of drawing an unusual sample. Also when you choose a significance level (α) this also creates the probability of making a Type I error.

9. Power and Type II Errors β A test’s ability to detect a false hypothesis is its power. When the null hypothesis is actually false, we hope our tests is strong enough to reject it. So β is the probability that the test fails to rejected a false null hypotheses. Power = 1- β. Whenever a study fails to reject its null hypothesis, the test’s power comes into question. Power is the test’s ability to reject the null hypothesis. This is important when the null hypothesis if false.

10. Reducing both Type I and Type II errors Reduce the likelihood of a Type II error by increasing sample size OR increasing the level of significance.

11. Discussion Questions Pg 506 of textbook D36. Explain why an increase in sample size increases the power of a test, all else remaining unchanged. Hint: Think about it, as if the null hypothesis was not correct. D37. What happens to the power of a test as the population proportion, p, moves farther away from the hypothesized value, p 0, all else remaining unchanged? Skip D38.

12. Explanation of D 36 and D 37 If it was false, the larger standard dev. of th smaller samples, increase the probability of a Type II error. Power – the ability of the test to accurately reject the null hypothesis.

13. 8.1 to 8.2 Review in class As part of a quality improvement program, your mail order company is studying the process of filling customer orders. According to company standards, an order is shipped on time if it is sent within 3 working days of the time it is received. You select a simple random sample (SRS) of 100 of the 5000 orders received in the past month for an audit. The audit reveals that 86 of these orders were shipped on time. Find a 95% confidence interval for the true proportion of the month’s orders that were shipped on time. Finish #2 and #3 in the next 15 minutes. If you finish early start the homework. 8.2 E #26 and 27 and # 34

14. 2.The estimate is 0.86, SE = 0.0347 so the 95% CI is 0.7920 to 0.9280.2. a)H 0 : p =.384 H A : p >.384 where p is the proportion of all free throws that Sue makes this season. b) The test statistic is Z = 3.13. c) The P-value is 0.0009. Reject the null hypothesis for a = 0.05; also at a = 0.01. d).4991 to.7509. There is strong evidence that Sue has improved. e) We must assume that the shots are equivalent to a random sample from all shots. Also, the sample size must be sufficiently large (which it is).

15. Work for P-value or Step #3 in a significance test

16. Answers continued… 3.The estimate is.173 with SE =.0437, so the 95% CI is 0.0877 to 0.2590. For the Quiz. Know all the vocabulary. Know the steps, conditions. Know how to find the confidence interval with your calculator AND by showing your work. Know how to do a one proportion z test with your calculator AND how to show your work for Part 3.

17. Directions for Quiz Read the problems carefully. Follow the steps reviewed in class for #2. For #2, set up the alternate hypothesis as not equal to the proportion

19. Answer to a.of A.P. Question continued… Confidence Interval Interpretation of interval Interpretation of confidence level

20. Answers to parts b. and c. b. c.