an N.49 Abstainers The Harvard study mentioned in the previ- f ous exercise estimated that 19 % of college students ab- stain from drinking alcohol. To estimate this proportion in your school, how large a random sample would you need to estimate it to within 0.05 with probability 0.95, if before conducting the study C 8.55 V unwilling to guess the proportion value at a. You are your school? h. You use the Harvard study as a guideline? Use the results from parts a and b to explain why strategy (a) is inefficient if you are quite sure you'll get a sample proportion that is far from 0.50. S S 0). ity S 8.50 How many businesses fail? mate the proportion of businesses started in the year 2006 that had failed within five years of their start-up. How large a sample size is needed to guarantee estimating this proportion correct to within a. 0.10 with probability 0.95? b. 0.05 with probability 0.95? c. 0.05 with probability 0.99? d. Compare sample sizes for parts a and b, and b and c, and summarize the effects of decreasing the margin of error and incre asing the confidence level. 851 Canada and the death penalty 1998 indicated that 48% of Canadians favor imposing the death penalty (Canada does not have it). A report by Amnesty International on this and related polls (www. amnesty.ca) did not report the sample size but stated, "Polls of this size are considered to be accurate within 2.5 percentage points 95% of the time." About how large was the sample size? 8.52 Farm size An estimate is needed of the mean acreage of farms in Ontario, Canada. A 95% confidence interval should have a margin of error of 25 acres. A study 10 he A study is planned to esti- on he еа 8.56 nts TRY en in f a or" ple hat ely ata led A poll in Canada in en 8.57 an vel of years ago or 200 acres for farm size. a. About hou in this province had a sample standard deviation 8.58 mmnle of farms is needed?