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Biostatistics Exercises

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1. (50 Points) In a national nutrition study 802 of 2306 sampled adults from Louisiana were obese, whereas 728 of 2358 sampled adults from Texas were obese. a. Perform the Z test to determine if there is a significant difference in the proportion of obese adults in Louisiana and Texas. b. Perform the chi-square test to determine if there is a significant difference in the proportion of obese adults in Louisiana and Texas. c. Demonstrate the equivalence of the tests in a. and b. d. Use a 95 % confidence interval to estimate the difference in the proportion of obese adults in Louisiana and Texas. e. Provide an interpretation of your interval. a. 𝐻0 : 𝑝𝐿𝑜𝑢𝑖𝑠𝑖𝑎𝑛𝑎 = 𝑝𝑇𝑒𝑥𝑎𝑠 𝐻𝐴 : 𝑝𝐿𝑜𝑢𝑖𝑠𝑖𝑎𝑛𝑎 ≠ 𝑝𝑇𝑒𝑥𝑎𝑠 802 = 0.3478 2306 728 𝑝𝑇𝑒𝑥𝑎𝑠 = 𝑝 ̂2 = = 0.3087 2358 𝑥1 + 𝑥2 802 + 728 1530 = 𝑝̂ = = = = 0.328 𝑛1 + 𝑛2 2306 + 2358 4664 𝑝𝐿𝑜𝑢𝑖𝑠𝑖𝑎𝑛𝑎 = 𝑝 ̂1 = z= ̂2 𝑝̂− 1 𝑝 1 √𝑝̂(1−𝑝̂)√𝑛 +𝑛 1 2 1 = 0.3478−0.3087 1 √0.328(1−0.328)√2306+2358 1 = 0.0391 √0.2204√0.00085774 = 2.84 Since the symbol in 𝐻𝐴 is “≠”, this is a two-tailed test. The critical value = 𝑍𝑐 = ±𝑍0.05/2 = ±1.96 As Z = 2.84 > 𝑍𝑐 , we reject 𝐻0 . At α = 0.05, we conclude that there is a significant difference in proportion of obese adults in Louisiana and Texas. b. Let r be obesity vs non ...
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