1. A clinical psychologist wants to estimate the average reaction time to a stimulus among N = 250 patients in a hospital specializing in nervous disorders. A simple random sample of n = 20 patients was selected, and their reaction times were measured, with the following results: = 2.1 seconds, s= 0.4 seconds Determine how large a sample should be taken in order to estimate the population mean, , with a bound on the error of estimation, B, of 1.0 seconds. Use 1.0 seconds as an approximation of the population standard deviation, .

2. An evaluator wants to determine the proportion of parents, p, who participate in musical activities (e.g., listening to music, discussing music) with their children at home at least once per week as part of an evaluation of a weekly preschool music program. The evaluator obtains a list of N = 500 parents whose children participate in the weekly music program. Determine the number of parents who need to be surveyed to estimate p with a bound on the error of estimation of B = 0.05. Assume that the evaluator has no prior information available to estimate p.

3. A study to assess the attitudes of accountants toward advertising their services involved sending questionnaires to n = 200 accountants selected from a list of N = 1,400 accountants. A total of n = 82 usable questionnaires were returned. The data summary for one question is shown in the accompanying table. All Respondents (82) Those Having Advertised in the Past (46) Virtual certainty 21 30 Very likely 5 10 Somewhat likely 19 30 About 18 20 Somewhat unlikely 5 10 Very unlikely 13 0 Absolutely not 15 0 No response 4 0 a. Estimate the population proportion, p, virtually certain to advertise in the future and place a bound on the error of estimation, B. b. Estimate the population proportion, p, having at least a 5050 chance of advertising in the future and place a bound on the error of estimation, B. c. Among those who advertised in the past, estimate the population proportion, p, somewhat unlikely to advertise again and place a bound on the error of estimation, B

4. A city planner is interested in estimating the total daily water consumed (in fluid ounces), , over a period of 4 weeks in a community during a dry spell. In the community, there are N = 1,000 households. Similar studies have found the population variance,v(y), to be approximately 36.00 (liters)2. Determine the sample size necessary to estimate the total water consumed over the 4 week period, p, with a bound on the error of estimation, B, equal to 1,000 fluid ounces.

6. A graduate program is interested in estimating the average annual income, , of its alumni. Although no prior information is available to estimate the population variance, ? 2 , it is known that most alumni incomes lie within a $10,000 range. The graduate program has N = 1,000 alumni. Determine the sample size necessary to estimate ? with a bound on the error of estimation of $500.

7. A graduate student in sociology intends to study alcohol consumption behaviors of undergraduate students at a small, private university using an internet survey. The graduate student obtains a list of all undergraduate student email addresses (N = 25,000). Determine the necessary sample size to estimate the proportion of students, p, who consume alcohol 3 or more times per week with a bound on the error of estimation, B, of 0.05. Prior studies suggest p to be approximately 30%. Determine how large a sample should be taken in order to estimate the population mean number of times per week that undergraduate students consume alcohol, ?, with a bound on the error of estimation, B, of 1.0 times per week. Use 1.7 times per week as an approximation of the population standard deviation,?. Which approach is more efficient in terms of the sample size necessary?