Homework6key

Homework6key - 1 Homework 6(15 pts 0.5 Bonus due Oct 14(0.5...

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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 two-sided 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 normal-weight 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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Homework6key - 1 Homework 6(15 pts 0.5 Bonus due Oct 14(0.5...

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