1. Warm-up Day of 8.1 and 8.2 Quiz and Types of Errors Notes

2. Answers to Inference and Proportions Worksheet 1.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).

3. Answers continued… 3.The estimate is.173 with SE =.0437, so the 95% CI is 0.0877 to 0.2590. Answer to A.P. Question a.

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

5. Answers to parts b. and c. b. c.

6. 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.

7. 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.

8. 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.

9. Reducing both Type I and Type II errors Reducing sample size is the best way to reduce a Type II error. The greater likelihood of Type I error, means the test has more power.

10. Discussion Questions Pg 506 of textbook D36. Explain why an increase in sample size increases the power of a test, all else remaining unchanged. 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? D38. Recall that the power of a test is the probability of rejecting the null hypothesis. Can a statistical test of the type discussed in this chapter ever have a power of 1? Can a statistical test of the type discussed in this chapter ever have a power of 0? If so, would either be desirable from a practical point of view

11. Vocabulary you should have for 8.1 8.1 level of confidence(capture rate), margin of error 8.2 significance test for a proportion, statistical significance, null hypothesis, alternate hypothesis, test statistic, p-value, critical values, level of significance, type 1 error, type 2 error, power of a test, one-sided, two-sided test 17 terms for 8.1 and 8.2

12. 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