b. 0.05 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 increasing the confidence level. 8.51 Canada and the death penalty A poll in Canada in 1008 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 years ago in this province had a sample standard deviation of 200 acres for farm size. a. About how large a sample of farms is needed? b. A sample is selected of the size found in part a. However, the sample has a standard deviation of 373 Choosing the Sample Size for a Study Section 8.4 300 acres rather than 200. What is the margin of error for a 95% confidence interval for the mean acreage y of farms? 8.53 Income of Native Americans How large a sample size TRY 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 an- nual income. We guess that nearly all of the incomes fall between $0 and $120,000 and that this distribution is ap- proximately bell shaped. Population variability the following statement: "In studies about a very diverse population, large samples are often necessary, for more homogeneous populations smaller samples are often adequate." Illustrate for the problem of estimating mean income for all medical doctors in the United States d to ore lts Explain the reasoning behind 8.54 whereas i- compared to estimating mean income for all entry-level employees at McDonald's restaurants in the United States. 8.55 Web survey to get large n gauge public opinion about legalization of marijuana. The sample size formula indicates that it need a random sam- ple of 875 people to get the desired margin of error. But surveys cost money, and it can only afford to randomly sample 100 people. Here's a tempting alternative: If it places a question about that issue on its website, it will get more than 1000 responses within a day at little cost. Is it s in ed fore A newspaper wants to l get