1. Tests about a Population Proportion Textbook Section 9.2

2. Carrying out a Significance Test Remember our basketball player who says he makes 80% of his free throws, but we think he’s exaggerating…? Let’s do a test: Step 1 – State Hypotheses and parameter H 0 : p = 0.80, where p = the actual proportion of free throws the shooter makes in the long run. H a : p < 0.80 Step 2: Check conditions Random? Stated in problem (usually but not always) Independent? 10% rule Sampling distribution Normal? n p & n (1 – p) ≥ 10 – SHOW WORK to prove!

3. Still Carrying out a Test

4. One Sample Z-test for Proportion

5. Check your understanding According the National Campaign to Prevent Teen and Unplanned Pregnancy, 20% of teens say that they have sent or posted sexually suggestive images of themselves. The counselor at a large high school worries that the actual figure may be higher. To find out she administers an anonymous survey to a random sample of 250 of the school’s 2800 students. All 250 respond, and 63 admit to sending or posting sexual images. Carry out a significance test at the 0.05 significance level. What conclusion should the counselor draw? CLICKER activity

6. Two-Sided Tests What if alternative hypothesis is p  ____? Nothing really changes in procedure EXCEPT wording of question and conclusion. Example: A news report claims that 75% of restaurant employees feel that work stress has a negative impact on their personal lives. A random sample of 100 employees finds that 68 answer yes. Is this good reason to think that the proportion of all employees differs from 0.75? H 0 : p = 0.75 H a : p  0.75 Conclusion: … evidence that the actual proportion differs from the claim of 75%

7. Significance Testing vs. Confidence Intervals Significance tests can provide evidence that a null hypothesis is likely incorrect, but it cannot give any information about the actual proportion in the population. A confidence interval can be helpful in giving us a smaller range of logical possibilities. Example: H 0 : p = 0.75; H a : p  0.75 P-value = 0.106 Confidence interval (0.588, 0.771) How does the confidence interval help give more information?

8. Type II Error & POWER Remember this? The more different the ACTUAL parameter is from the null hypothesis, the lower the probability of making a Type II Error. The probability that a test does reject the null when it is in fact false is called POWER Truth about the Population H 0 TrueH 0 False Conclusion Based on Sample Reject H 0 Type I ErrorCORRECT Fail to Reject H 0 CORRECTType II Error POWER

9. Type II Errors & Power cont’d

10. What affects Power?

11. Check your Understanding