Lab 8b for Math 17 Hypothesis Testing II

Lab 8b for Math 17: Hypothesis Testing II 1 Projects Introduced - See Other Handout 2 Ear Infections (Data from Uhari 1998, discussed in Utts/Heckard) Preschool children participated in a study to test the effectiveness of the sweetener Xylitol in preventing ear infections. 165 children received placebo daily doses and 68 of them got an ear infection during the study (three month duration). Another 159 children received Xylitol daily doses and 46 got an ear infection during the study. The study was a randomized experiment. a. Obtain a 90 percent confidence interval for the difference between proportions of ear infections between placebo and Xylitol groups. Be sure to check assumptions. b. Interpret your interval. c. Interpret the confidence level. d. If someone told you that one of the assumptions for this CI was that the populations were normally distributed, how would you explain that assumption does not make sense? 1 e. Would you be able to conclude that there is no difference between the placebo and Xylitol groups based on the CI? What significance level is associated with that decision? Would you be able to conclude that Xylitol is more effective than placebo at reducing the risk of ear infection? What significance level is associated with that decision? Explain. f. Now, perform a hypothesis test to test whether Xylitol is more effective than placebo at reducing the risk of ear infection. Choose a significance level that makes the test equivalent to your confidence interval as determined in e. Verify that you reach the same conclusion with your hypothesis test as with the CI. g. What is the distribution of the test statistic assuming the null hypothesis is true? (I.E. What distribution did you use to find the p-value?) 2 3 Correcting a Hypothesis Test - To Turn In You stumble upon a crumbled piece of paper that appears to have been dropped by another intro stats student. The paper has a partial homework problem on it, but the context is lost as it is just their scratchwork. Based on the scratchwork below, can you help them correct any issues before they make their final writeup? 1-sample t-test for population mean 1. Hypotheses: H0 : µ = 3200 vs. HA : x̄ < 3200 2. Conditions: RS is stated. Need to check ten successes and ten failures. ??? (previous line has been crossed out and erased a few times) 3. Mechanics. x̄ = 3100 and s = 250 with an n = 100. z= x̄ − µ0 100 3100 − 3200 √ = = =4 250/10 25 s/ n Use t distribution with 99 df for p-value. 99 not in table so round up to df=100. p-value is greater than 1-.005, so greater than .995, which is huge. 4. Conclusion (Decision): (Do not reject null hypothesis). We do not have evidence to conclude the mean crop output has decreased from last year’s average of 3200. 3