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www.downloadslide.com Supplementary Exercises 439 8.107 Refer to Exercise 8.106. Suppose that you plan to estimate the difference in the survival rates of seeds for male parents in low-water and low-nutrient environments to **with**in .03 **with** probability .95. If you plan to use an equal number of seeds from male parents in each environment (that is, n 1 = n 2 ), how large should n 1 and n 2 be? 8.108 A chemist who has prepared a product designed to kill 60% of a particular type of insect wants to evaluate the kill rate of her preparation. What sample size should she use if she wishes to be 95% confident that her experimental results fall **with**in .02 of the true fraction of insects killed? 8.109 To estimate the proportion of unemployed workers in Panama, an economist selected at random 400 persons from the working class. Of these, 25 were unemployed. a Estimate the true proportion of unemployed workers and place bounds on the error of estimation. b How many persons must be sampled to reduce the bound on the error of estimation to .02? 8.110 Past experience shows that the standard deviation of the yearly income of textile workers in a certain state is $400. How many textile workers would you need to sample if you wished to estimate the population mean to **with**in $50.00, **with** probability .95? 8.111 How many voters must be included in a sample collected to estimate the fraction of the popular vote favorable to a presidential candidate in a national election if the estimate must be correct to **with**in .005? Assume that the true fraction lies somewhere in the neighborhood of .5. Use a confidence coefficient of approximately .95. 8.112 In a poll taken among college students, 300 of 500 fraternity men favored a certain proposition whereas 64 of 100 nonfraternity men favored it. Estimate the difference in the proportions favoring the proposition and place a 2-standard-deviation bound on the error of estimation. 8.113 Refer to Exercise 8.112. How many fraternity and nonfraternity men must be included in a poll if we wish to obtain an estimate, correct to **with**in .05, for the difference in the proportions favoring the proposition? Assume that the groups will be of equal size and that p = .6 will suffice as an approximation of both proportions. 8.114 A chemical process has produced, on the average, 800 tons of chemical per day. The daily yields for the past week are 785, 805, 790, 793, and 802 tons. Estimate the mean daily yield, **with** confidence coefficient .90, from the data. What assumptions did you make? 8.115 Refer to Exercise 8.114. Find a 90% confidence interval for σ 2 , the variance of the daily yields. 8.116 Do we lose our memory capacity as we get older? In a study of the effect of glucose on memory in elderly men and women, C. A. Manning and colleagues 18 tested 16 volunteers (5 men and 11 women) for long-term memory, recording the number of words recalled from a list read to each person. Each person was reminded of the words missed and was asked to recall as many words as possible from the original list. The mean and standard deviation of the long-term word memory scores were y = 79.47 and s = 25.25. Give a 99% confidence interval for the true long-term word memory scores for elderly men and women. Interpret this interval. 8.117 The annual main stem growth, measured for a sample of 17 4-year-old red pine trees, produced a mean of 11.3 inches and a standard deviation of 3.4 inches. Find a 90% confidence interval for the mean annual main stem growth of a population of 4-year-old red pine trees subjected to similar environmental conditions. Assume that the growth amounts are normally distributed. 18. Source: C. A. Manning, J. L. Hall, and P. E. Gold, “Glucose Effects on Memory and Other Neuropsychological Tests in Elderly Humans,” Psychological Science 1(5) (1990).

www.downloadslide.com 440 Chapter 8 Estimation 8.118 Owing to the variability of trade-in allowance, the profit per new car sold by an automobile dealer varies from car to car. The profits per sale (in hundreds of dollars), tabulated for the past week, were 2.1, 3.0, 1.2, 6.2, 4.5, and 5.1. Find a 90% confidence interval for the mean profit per sale. What assumptions must be valid for the technique that you used to be appropriate? 8.119 A mathematics test is given to a class of 50 students randomly selected from high school 1 and also to a class of 45 students randomly selected from high school 2. For the class at high school 1, the sample mean is 75 points, and the sample standard deviation is 10 points. For the class at high school 2, the sample mean is 72 points, and the sample standard deviation is 8 points. Construct a 95% confidence interval for the difference in the mean scores. What assumptions are necessary? 8.120 Two methods for teaching reading were applied to two randomly selected groups of elementary schoolchildren and were compared on the basis of a reading comprehension test given at the end of the learning period. The sample means and variances computed from the test scores are shown in the accompanying table. Find a 95% confidence interval for (µ 1 − µ 2 ). What assumptions are necessary? Statistic Method 1 Method 2 Number of children in group 11 14 y 64 69 s 2 52 71 8.121 A comparison of reaction times for two different stimuli in a psychological word-association experiment produced the results (in seconds) shown in the accompanying table when applied to a random sample of 16 people. Obtain a 90% confidence interval for (µ 1 − µ 2 ). What assumptions are necessary? Stimulus 1 Stimulus 2 1 2 4 1 3 1 2 2 2 3 3 3 1 2 3 3 8.122 The length of time between billing and receipt of payment was recorded for a random sample of 100 of a certified public accountant (CPA) firm’s clients. The sample mean and standard deviation for the 100 accounts were 39.1 days and 17.3 days, respectively. Find a 90% confidence interval for the mean time between billing and receipt of payment for all of the CPA firm’s accounts. Interpret the interval. 8.123 Television advertisers may mistakenly believe that most viewers understand most of the advertising that they see and hear. A recent research study asked 2300 viewers above age 13 to look at 30-second television advertising excerpts. Of these, 1914 of the viewers misunderstood all or part of the excerpt they saw. Find a 95% confidence interval for the proportion of all viewers (of which the sample is representative) who will misunderstand all or part of the television excerpts used in this study. 8.124 A survey of 415 corporate, government, and accounting executives of the Financial Accounting Foundation found that 278 rated cash flow (as opposed to earnings per share, etc.) as the most important indicator of a company’s financial health. Assume that these 415 executives constitute a random sample from the population of all executives. Use the data to find a 95% confidence

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