Name_______________________ Fall 2010 Chapter 8 Math 54 Dr. McGraw Th sh is ar stu ed d vi y re aC s ou ou rc rs e eH w er as o. co m 1. A recent General Social Survey asked, \"During the last year, did anyone take something from you by using force - such as a stick up, mugging, or threat?\" Of 987 subjects, 17 answered yes and 970 answered no. a. Find a point estimate of the proportion of the population who were victims. b. Find the standard error of this estimate. c. Find the margin of error for a 95% confidence interval. d. Construct the 95% confidence interval for the population proportion. e. Can you conclude that fewer than 10% of all adults in the United States were victims? 1 https://www.coursehero.com/file/9155573/Chapter-8-questions-from-Agresti/ Th sh is ar stu ed d vi y re aC s ou ou rc rs e eH w er as o. co m 2. A study compared various therapies for teenage girls suffering from anorexia, an eating disorder. For each girl, weight was measured before and after a fixed period of treatment. The variable measured was the change in weight, X = weight at the end of the study minus weight at the beginning of the study. The therapies were designed to aid weight gain, corresponding to positive values X. For the sample of 17 girls receiving the family therapy, the changes in weight during the study were 11, 11, 6, 9, 14, -3, 0, 7, 22, -5, 04, 12, 13, 9, 4, 5, 11 a. Plot these with a dot plot or box-plot, and summarize. b. Find the mean and standard deviation for this sample. c. Find the standard error of the mean (se) d. Find the critical value (t-score) that you will need to use to find the 95% confidence interval. e. Find the 95% confidence interval for the true mean change in weight for the subjects in this study. 2 https://www.coursehero.com/file/9155573/Chapter-8-questions-from-Agresti/ 3. The following is data on how often a subject reads a newspaper. Variable N Mean Std Dev News 60 4.1 3.0 SE Mean 0.387 95.0% CI (3.325, 4.875) Th sh is ar stu ed d vi y re aC s ou ou rc rs e eH w er as o. co m a. Is it plausible that the population mean is 7? Explain b. Suppose that the sample size has been 240, with a mean of 4.1 and s = 3.0. Find a 95% confidence interval, and compare it to the one reported. Describe the effect of sample size on the margin of error. c. Does it seem plausible that the population distribution of this variable is normal? Why? d. Explain the implications of the term \"robust\" regarding the normality assumption made to conduct this analysis. 3 https://www.coursehero.com/file/9155573/Chapter-8-questions-from-Agresti/ sh is ar stu ed d vi y re aC s ou ou rc rs e eH w er as o. co m 4. A Harvard Study estimated that 19% of college students abstain from drinking alcohol. To estimate this proportion in your school, how large a random sample would you need to estimate it within 0.05 with a probability of .95, if before conducting the study a. You are unwilling to predict the proportion value at your school? b. You use the Harvard study as a guideline? c. Use the results from (a) and (b) to explain why the strategy is inefficient if you are quite sure you'll get a sample proportion that is far from 0.50. Th 5. How large of a sample size do we need to estimate the mean annual income of Native Americans in Onondaga County, New York, correct to within $1000 with probability 0.99? No information is available to us about the standard deviation of their annual income. We that that nearly all of the incomes fall between $0 and $120,000 and that this distribution is approximately bell shaped. 4 https://www.coursehero.com/file/9155573/Chapter-8-questions-from-Agresti/ Powered by TCPDF (www.tcpdf.org)