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Unformatted text preview: 1 Homework 6 (15 pts + 0.5 Bonus) due Oct. 14 (0.5 pts.) 7.22. The associated Press (Dec. 16, 1991) reported that in a sample of 507 adult Americans, only 142 correctly described the Bill of Rights as the first ten amendments to the U.S. Constitution. Calculate a twosided confidence interval using a 99% confidence level for the proportion of all U.S. adults that could give a correct description of the Bill of Rights. = 142 507 = 0.280, ?? = 2.576 + ( ?? ) 2 2 ?? (1 ) + ( ?? ) 2 4 2 1 + ( ?? ) 2 = 0.280 + (2.576) 2 2(507) 2.576 (0.280)(1 0.280) 507 + (2.576) 2 4(507) 2 1 + (2.576) 2 507 = 0.280 + 0.006544 2.576 0.0003976 + 0.000006454 1 + 0.01309 = 0.2865 0.05172 1.01309 (0.232,0.334) Note: this number is different from the one using the condensed formula: ?? (1 ) = 0.280 2.576 0.280(1 0.280) 507 = 0.280 0.05137 (0.229,0.331) (0.5 pts.) 7.24. A random sample of 487 nonsmoking women of normal weight who had given birth at a large metropolitan medical center was selected. It was determined that 7.2% of these births resulted in children of low birth weight. Calculate the upper confidence bound using a confidence level of 99% for the proportion of all such births that result in children of low birth weight. z crit = 2.326 + ( ?? ) 2 2 + ?? (1 ) + ( ?? ) 2 4 2 1 + ( ?? ) 2 = 0.072 + (2.326) 2 2(487) + 2.326 (0.072)(1 0.072) 487 + (2.326) 2 4(487) 2 1 + (2.326) 2 487 = 0.072 + 0.0055547 + 2.326 0.0001372 + 0.000005703 1 + 0.01111 = 0.077555 + 0.027805 1.01111 = 0.104 2 Note: this number is different from the one using the condensed formula: + ?? (1 ) = 0.072 + 2.326 0.072(1 0.072) 487 = 0.072 + 0.0272 = 0.099 (0.5 pts.) 7.26. The article in Exercise 24 stated that 6.8% of a sample of 503 nonsmoking obese women gave birth to children of low birth weight. Calculate a 95% lower confidence bound for the difference between the population proportion of normalweight nonsmoking women and the population proportion of obese nonsmoking women who give birth to children of low birth weight. Hint: p 1 p 2 has a approximately normal distribution in the sample sizes are sufficiently large (same criteria as for one sample) with ? = ? and ? = ( ) + ? ( ? ) ? . 1: nonsmoking normal weight women, 2: nonsmoking obese women z crit = 1.960 1 2 ??...
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