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Ch. 7 – Estimates and Sample Sizes 1. The mean and standard deviation, respectively, of students working after school are 17.6h and 9.3h. The given statistics are based on a sample size of 50 drawn from a normally distributed population. a. Find the best point estimate of the population mean. b. Find a 95% confidence interval estimate of the population mean. Use: • AND ̅ ̅ √ c. When do you use the Student 2. Find the value of (A) (B) (C) (D) distribution, instead of a distribution? that corresponds to a confidence level of 97.80%. 2.29 0.011 2.01 2.29 3. How many students must be surveyed if a psychologist wants 96% confidence that a sample proportion is in error by no more than .06? Use: OR . 4. Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation . Assume that the population has a normal distribution. College students' annual earnings: 98% confidence; 9, ̅ $3705, $841 (A) (B) (C) (D) $568 $511 $662 $531 $1611 $1646 $1097 $1854 5. The Newton Car Park is a dealership considering newspaper advertising targeted at women buyers. A marketing study found that 312 of 650 randomly selected buyers of compact cars were women (based on the Ford Motor Company). Construct a 95% interval estimate for the true percentage of all compact car buyers who are women. ̂ ̂ ̂ 6. 364 randomly selected light bulbs were tested in a laboratory, 124 lasted more than 500 hours. Find a point estimate of the proportion of all light bulbs that last more than 500 hours. (A) (B) (C) (D) 0.338 0.341 0.254 0.659 7. A sociologist develops a test to measure attitudes about public transportation, and 25 randomly selected subjects are given the test. Their mean score is 76.2 and their population standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects. Use • and ̅ ̅ √ 8. Assume that a sample is used to estimate a population proportion . Find the margin of error that corresponds to the given statistics and confidence level. 95% confidence; the sample size is 6100, of which 40% are successes (A) 0.00923 (B) 0.1041 (C) 0.1062 (D) 0.1023 9. A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be bell-shaped with a mean of $9004 and a standard deviation of $5629. Construct the 99% confidence interval for the mean of all such costs. If you are a manager for an insurance company that provides lower rates for drivers who wear seat belts, and you want a conservative estimate for a worst-case scenario, what amount should you use as the possible hospital cost for an accident victim who wears seat belts? • ̅ ̅ √ 10. Find the critical value 95 percent. (A) (B) (C) (D) corresponding to a sample size of 4 and a confidence level of 0.216 0.352 9.348 7.815 11. Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution. 12, ̅ 21.9, 4.0 , 99% confidence (A) (B) (C) (D) 18.31 18.24 18.33 18.76 25.49 25.56 25.47 25.04 12. Of 366 randomly selected medical students, 27 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community. (A) (B) (C) (D) 0.0513 0.0386 0.0470 0.0419 0.0962 0.109 0.101 0.106