7-2 Estimating a Population Mean 329 38.Women Who Give Birth An epidemiologist plans to conduct a survey to estimate the percentage of women who give birth. How many women must be surveyed in order to be 99% confident that the estimated percentage is in error by no more than two percentage points? a. Assume that nothing is known about the percentage to be estimated. b. Assume that a prior study conducted by the U.S. Census Bureau showed that 82% of women give birth. c. What is wrong with surveying randomly selected adult women? 7-1 Beyond the Basics 39.Finite Population Correction Factor For Formulas 7-2 and 7-3 we assume that the population is infinite or very large and that we are sampling with replacement. When we sample without replacement from a relatively small population with size N, we modify E to include the finite population correction factor shown here, and we can solve for n to obtain the result given here. Use this result to repeat part (b) of Exercise 38, assuming that we limit our population to a county with 2500 women who have completed the time during which they can give birth. E = za>2Bpnqn n BN - n N - 1 n = Npnqn3z a>24 2 pnqn3z a>24 2 + 1N - 12E2 40.One-Sided Confidence Interval A one-sided claim about a population proportion is a claim that the proportion is less than (or greater than) some specific value. Such a claim can be formally addressed using a one-sided confidence interval for p, which can be expressed as p 6 pn + E or p 7 pn - E, where the margin of error E is modified by replacing z a>2 with za. (Instead of dividing a between two tails of the standard normal distribution, put all of it in one tail.) The Chapter Problem refers to a Sallie Mae survey of 950 undergraduate students, and 53% of the survey subjects take online courses. Use that data to construct a one-sided 95% confidence interval that would be suitable for helping to determine whether the percentage of all undergraduates who take online courses is greater than 50%. 41.No Failures According to the Rule of Three, when we have a sample size n with x = 0 successes, we have 95% confidence that the true population proportion has an upper bound of 3>n. (See “A Look at the Rule of Three,” by Jovanovic and Levy, American Statistician, Vol. 51, No. 2.) a. If n independent trials result in no successes, why can’t we find confidence interval limits by using the methods described in this section? b. In a study of failure rates of computer hard drives, 45 Toshiba model MD04ABA500V hard drives were tested and there were no failures. What is the 95% upper bound for the percentage of failures for the population of all such hard drives? Key Concept The main goal of this section is to present methods for using a sample mean x to make an inference about the value of the corresponding population mean m. There are three main concepts included in this section: ■ Point Estimate: The sample mean x is the best point estimate (or single value estimate) of the population mean m. ■ Confidence Interval: Use sample data to construct and interpret a confidence interval estimate of the true value of a population mean m. ■ Sample Size: Find the sample size necessary to estimate a population mean. 7-2 Estimating a Population Mean
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