1. Warm-up 8.2 Testing a proportion Data Analysis 9 If ten executives have salaries of $80,000, six salaries of $75,000, and three have salaries of $70,000, what is the median salary? A. $75,000 B. $76,842 C. $77,500 D. $80,000 E. None of the above Experimental Design 14 In general, for a survey to yield unusable results: I. A sample size of n = 30 is usually sufficient. II. Researchers must be careful in the way questions are worded. III. Researchers must carefully choose people who they think are representative of the population. A. I only B. II only C. III only D. II and III E. I, II, and III

4. Inference for Distributions Sample Proportion Sample Mean (known ) Sample Mean (unknown ) General formula Specific formula Expanded formula Calc Function1-Prop Z IntervalZ intervalT Interval Confidence Intervals 8.2 Testing a Proportion 9.1 Confidence Interval of the Mean 9.2 Significance Testing for the Mean

5. Answers to 8.1 E #7 – 10, 16 and 17 E#7. The randomization condition is met since the teens were randomly selected. A sample of 549 is less than 10% of the population of teens in the U.S.. 52% of 549 is 285.48 > 10 and 48% of 549 is 263.52 > 10 so it meets the success/failure condition.

6. E#8 The sample was not random. 885 is less than 10% of the population. Both 40% and 60% of 885 are greater than 10.

7. E #9 The diagram of 8.2 can not be used because the graph on the right is for a sample size of 40 and not for 100. A sample size of 100 would have a smaller confidence interval. E #10 For a sample size of 40 and a proportion of 5%, the 8.2 diagram could be used. The only issue is that a sample size of 40 is not big enough to meet the success failure condition. 40 (0.05) = 8 < 10

8. E #16. Since the margin of error is to make it one quarter of its original size, the sample size has to be 16 times greater. E#17. A, D, F and H are correct interpretations

9. Hypothesis Testing We will now watch a video called P-value Extravaganza FYI: The guys are drinking soda in the video.

10. 8.2 Significance Test Jenny and Maya wonder if heads and tails are equally likely when a penny is spun. They spin pennies 40 times and get 17 heads. Later… Miguel and Kevin spin pennies and get 10 heads out of 40 spins for a sample proportion, p-hat of 0.25. A sample proportion is said to be statistically significant ifstatistically significant it isn’t a reasonably likely outcome when the proposed standard is true.

11. P-values Instead of simply reporting whether a result is statistically significant, it is common practice also to report a P-value. The P-value for a test is the probability of seeing a result from aP-value random sample that is as extreme as or more extreme than the result you got from your random sample if the null hypothesis is true. Find the P-value for Jenny and Maya. They spin pennies 40 times and get 17 heads. A large P-value tells you that the sample proportion you observed is near p 0, so your result isn’t statistically significant.

12. Finding Critical Values Suppose you want to reject the null hypothesis when the test statistic, z, is in the outer 10% of the standard normal distribution—that is, with a level of significance equal to 0.10. What should you use as critical values? α = 0.1

13. To reject or not to reject In a courtroom, a defendant is either guilty or not guilty. Notice they don’t say innocent. Same with the null hypothesis. Either reject the null hypothesis or fail to reject the null hypothesis. The rejection or lack of rejection is based on the p-value and whether or not it is statistically significant.

14. Pg 498 Components of Significant Test 1. Give the name of the test and check the conditions for its use. For a significance test for a proportion, three conditions must be met: The sample is a simple random sample from a binomial population. Both np 0 and n(1 − p 0 ) are at least 10. The population size is at least 10 times the sample size. 2. State the hypotheses, defining any symbols. When testing a proportion, the null hypothesis, H 0, isH 0 : The percentage of successes, p, in the population from which the sample came is equal to p 0.The alternative hypothesis, H a, can be of three forms:

15. Components continued… 3. Compute the test statistic, z, and find the critical values, z*, and the P-value. Include a sketch that illustrates the situation. If the alt. hypothesis is ≠, the α is applied to two sides. 4. Write a conclusion. There are two parts to stating a conclusion: Compare the value of z to the predetermined critical values, or compare the P-value to α. Then say whether you reject the null hypothesis or don’t reject the null hypothesis, linking your reason to the P-value or to the critical value.

16. Problem 1: A large city’s Dept. of Motor Vehicles claimed 80% of candidates pass the driving test, but newspaper reports of 90 randomly selected local teens who had taken the test only 61 passed. STEP 1: STEP 1: Check the 3 conditions then give the name of the test you are about to perform. STEP 2: STEP 2: State the hypothesis. (Null and possible Alternative Hypothesis)

17. STEP 3: STEP 3: Calculate the critical value, test statistic and p-value. *Demonstrate these with a sketch of the distribution curve as well! STEP 4: STEP 4: Write a conclusion. Include an explanation of the p value in context and in the format of a ratio. Because the P-value of 0.002 is very low, I reject the null hypothesis in favor of the alternate hypothesis. These survey data provide strong evidence that the passing rate for teenagers taking the driving test is lower than 80%. If the passing rate for teenage driving candidates were actually 80%, we’d expect to see success rates this low in only about 1 in 500 (0.2%). This seems quite unlikely, casting doubt that the DMV’s stated success rate applies to teens.

18. Problem 2 Advances in medical care such as prenatal ultrasound examination now makes it possible to determine a child’s sex early in the pregnancy. A study from Punjab, India reports that, in 1993, one hospital reported 56.9% boys in 550 live births. It’s a medical fact that male babies are slightly more common than female babies. The baseline is 51.7% boys in all live births. Use α = 0.1. Is this a one-tailed or two-tailed significance test? STEP 1: STEP 1: Check the 3 conditions then give the name of the test you are about to perform. H.W. P#20, 23 and 24

19. STEP 2: STEP 2: State the hypothesis. (Null and possible Alternative Hypothesis) STEP 3: STEP 3: Calculate the critical value, test statistic and p-value. *Demonstrate these with a sketch of the distribution curve as well! STEP 4: STEP 4: Write a conclusion.

20. Things to watch for with one proportion significance test Don’t base your null hypothesis on what you see in the data (p-hat). Don’t base your alternative hypothesis on the data (p-hat). Don’t forget to check the conditions. Don’t accept the alternate hypothesis. If you fail to reject the null hypothesis, don’t think a bigger sample would be more likely to lead to a rejection.

21. Ch. 7 Test Since 8.1,8.2, 9.1 and 9.2 takes the concepts in Ch. 7 further, I will replace your Ch. 7 test score with your test score from the next test. The only common mistake I noticed on the test was that sometimes you forget for a sampling distribution you have to adjust the S.E.. And you adjust the S.E. using the information from the population.