Nonparametrics Math 216 Exam 1 October 22 2004 Prof Hartlaub Name This exam is open book open notes but you must show all of your work to receive full credit The point values for each problem are provided in parentheses Solve all of the problems below 1 One of the important issues for poultry farmers is the production rate the percentage of days on which a given hen actually lays an egg Ideally that would be 100 an egg every day but realistically hens tend to lay eggs on about 3 of every 4 days A particular company ISA Babcock wants to advertise the production rate for a mature B300 Layer as a 95 confidence interval with a margin of error of 2 How many hens must they collect data on 10 2 Nationwide it is estimated that 40 of service stations have gas tanks that leak to some extent A new program in California is designed to lessen the prevalence of these leaks We want to assess the effectiveness of the program by seeing if the percentage of service stations whose tanks leak has decreased To do this we randomly sample 27 service stations in California and determine whether there is evidence of leakage In our sample seven of the stations exhibit any leakage a Is there evidence that this new program is effective Be sure to state your hypotheses provide a test statistic and p value and specify your conclusion 15 b If the new program actually works have you made an error If so what kind 5 3 Who reads the newspaper more men or women Eurostat an agency of the European Union EU conducts surveys on several aspects of daily life in EU countries Recently an agency asked samples of 1000 respondents in each of 14 European countries whether they read the newspaper on a daily basis The data are provided by country and gender below and in p data math nonparametrics newspaper mtw Country Belgium Denmark Germany Greece Spain Ireland Italy Luxembourg Netherlands Austria Portugal Finland Sweden UK Men 56 3 76 8 79 9 22 5 46 2 58 0 50 2 71 0 71 3 78 2 58 3 93 0 89 0 32 6 Women 45 5 70 3 76 8 17 2 24 8 54 0 29 8 67 0 63 0 74 1 24 1 90 0 88 0 30 4 a Identify the appropriate parameter s of interest to the researchers 5 b Provide point and interval estimates that can be used to address the research question of interest Be sure to identify your confidence level describe how the estimates are calculated interpret your interval and answer the research question 25 4 The number of calories per serving for different brands of strawberry and vanilla yogurt is shown below and provided in p data math nonparametrics yogurt mtw Row 1 2 3 4 5 6 7 8 9 10 11 12 Brand America s Choice Breyer s Lowfat Columbo Dannon Light n Fit Dannon Lowfat Dannon laCreme Great Value La Yogurt Mountain High Stonyfield Farm Yoplait Custard Yoplait Light Stawberry 210 220 220 120 210 140 180 170 200 100 190 100 Vanilla 200 220 180 120 230 140 80 160 170 120 190 100 a Do these data suggest that there is a significant difference in calories between servings of strawberry and vanilla yogurt Test the appropriate hypotheses and state your conclusion 15 b A diet guide claims that you will get 120 calories from a serving of vanilla yogurt Assuming that the distribution of calories in vanilla yogurt is symmetric create an interval estimate that can be used to test this claim Be sure to identify your confidence level describe how your estimate is calculated interpret your interval and state your conclusion 15 5 An experiment was performed to see whether sensory deprivation over an extended period of time has any effect of the alpha wave patterns produced by the brain To determine this 20 subjects inmates in a Canadian prison were randomly split into two groups Members of one group were placed in solitary confinement Those in the other group were allowed to remain in their own cells Seven days later alpha wave frequencies were measured for all subjects The data are provided in the table below and in p data math nonparametrics brain mtw Nonconfined Confined 10 7 9 6 10 7 10 4 10 4 9 7 10 9 10 3 10 5 9 2 10 3 9 3 9 6 9 9 11 1 9 5 11 2 9 0 10 4 10 9 a Perform the appropriate test Be sure to specify the appropriate null and alternative hypotheses provide the test statistic and p value and state your conclusion 15 b A researcher is interested in formally testing the hypothesis that the variability in the alpha wave frequencies is the same for these two groups Which test would you recommend Why Do NOT conduct the test 10 c Another researcher is interested in testing for a shift difference in the alpha wave frequencies for the two groups She suspects that the alpha wave frequencies for the confined group will be shifted to the left of those for the nonconfined group Do the data provide significant evidence to support her suspicion Be sure to specify the appropriate null and alternative hypotheses provide the test statistic and p value and state your conclusion 15