Eggs are an excellent source of choline and selenium and a good source of high-quality protein,...

 

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Eggs are an excellent source of choline and selenium and a good source of high-quality protein, vitamin D, vitamin B12, phosphorus, and riboflavin. Eggs also come in various sizes, such as large and extra-large. A nutritionist wants to quantify the nutritional value of a large egg but needs to know the average weight of large eggs in order to accurately report the nutritional value. The following data represent egg weights (in grams) for a sample of 10 eggs. These data are consistent with summary quantities in the paper "Evaluation of Egg Quality Traits of Chickens Reared under Backyard System in Western Uttar Pradesh".† 53.04, 53.51, 52.53, 53.01, 53.05, 52.85, 52.64, 53.22, 53.24, 53.15 (a) Calculate the point estimate (in grams) for the population mean. Calculate its margin of error (in grams) at 95% confidence. Assume that = 0.274. (Use a table or technology. Round your answer to three decimal places.) g (b) Calculate a 95% confidence interval for the true mean weight (in grams) of all extra-large eggs. Assume that o = 0.274. (Round your answers to three decimal places.) (c) Suppose that the nutritionist would like to cut the margin of error in half. What sample size should be used? a. 10 b. 20 c. 30 d. 40 (d) Which of the following combinations of confidence level and sample size will produce the smallest margin of error when estimating the true mean when σ is known? a. 85%, 35 b. 85%, 125 c. 90%, 125 d. 90%, 35 (e) Which of the following combinations of population standard deviation and sample size will produce the smallest margin of error when estimating the true mean when o is known? a. 0.53, 35 b. 0.41, 35 c. 0.41, 125 d. 0.53, 125 Eggs are an excellent source of choline and selenium and a good source of high-quality protein, vitamin D, vitamin B12, phosphorus, and riboflavin. Eggs also come in various sizes, such as large and extra-large. A nutritionist wants to quantify the nutritional value of a large egg but needs to know the average weight of large eggs in order to accurately report the nutritional value. The following data represent egg weights (in grams) for a sample of 10 eggs. These data are consistent with summary quantities in the paper "Evaluation of Egg Quality Traits of Chickens Reared under Backyard System in Western Uttar Pradesh".† 53.04, 53.51, 52.53, 53.01, 53.05, 52.85, 52.64, 53.22, 53.24, 53.15 (a) Calculate the point estimate (in grams) for the population mean. Calculate its margin of error (in grams) at 95% confidence. Assume that = 0.274. (Use a table or technology. Round your answer to three decimal places.) g (b) Calculate a 95% confidence interval for the true mean weight (in grams) of all extra-large eggs. Assume that o = 0.274. (Round your answers to three decimal places.) (c) Suppose that the nutritionist would like to cut the margin of error in half. What sample size should be used? a. 10 b. 20 c. 30 d. 40 (d) Which of the following combinations of confidence level and sample size will produce the smallest margin of error when estimating the true mean when σ is known? a. 85%, 35 b. 85%, 125 c. 90%, 125 d. 90%, 35 (e) Which of the following combinations of population standard deviation and sample size will produce the smallest margin of error when estimating the true mean when o is known? a. 0.53, 35 b. 0.41, 35 c. 0.41, 125 d. 0.53, 125

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