1. In planning a study of the birth weights of babies whose mothers did not see a doctor before delivery, a researcher states their hypotheses as: Ho: :2 = 1000 g Ha: f or 0.05. c. In using a 95% confidence interval to test Ho:u=10 against Ha: u # 10 p>0.05 if HO is any of the numbers inside the confidence interval. d. In using a 95% confidence interval to test Ho:u=10 against Ha: u # 10 p>0.05 if HO is any of the numbers outside the confidence interval. 7. True or False (1/2 point each) 1. T F One-tailed tests provide stronger evidence against the null than two-tailed tests. ii. T F If we reject the null hypothesis we have proven that the null hypothesis is false. iii. TF If we retain the null hypothesis we have proven that the null hypothesis is true. iv . T F In very large samples even very small effects can be statistically significant. V . T F In very small samples even very large effects can fail to be statistically significant. vi. TF The p-value tells us the magnitude of the effect. If a test is statistically significant it means the effect is large enough to be meaningful and have practical significance. 8. A research report described two studies that both achieved statistical significance at the 5% level. The p- value for the first is 0.049; for the second it is 0.0002. Do the p-values add any useful information beyond that conveyed by the statement that both results are statistically significant? Explain. (1 point) Bonus Question A group of psychologists once measured 77 variables on a sample of schizophrenic people and a sample of people who were not schizophrenic. They compared the two samples using 77 separate significance tests. Two of these tests were significant at the 5% level (alpha=.05). Suppose that there is in fact no difference in any of the variables between people who are and people who are not schizophrenic, so that all 77 null hypotheses are true. i. What is the probability that one specific test shows a difference significant at the 5% level (alpha=.05)? ii. Why is it not surprising that 2 of the 77 tests were significant at the 5% level (alpha=.05)? Hint: How many tests would you expect to be significant just due to random sampling variability