20. Working at home: According to the U.S. Census Bureau, 43% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 162 were college graduates. a. Find a point estimate for the proportion of college graduates among women who work at home. b. Construct a 98% confidence interval for the proportion of women who work at home who are college graduates. c. Based on the confidence interval, is it reasonable to believe that the proportion of college graduates among women who work at home is the same as the proportion of college graduates among men who work at home? Explain. 28. Reading proficiency: An educator wants to construct a 98% confidence interval for the proportion of elementary schoolchildren in Colorado who are proficient in reading. a. The results of a recent statewide test suggested that the proportion is 0.70. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.05? b. Estimate the sample size needed if no estimate of p is available. c. If the educator wanted to estimate the proportion in the entire United States rather than in Colorado, would the necessary sample size be larger, smaller, or about the same? Explain.
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Working at home: According to the U.S. Census Bureau, 33% of men who worked at home were college graduates. In a sample of 474 women who worked at home, 155 were college graduates. Part 1 of 3: (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is 0.327. Part 2 of 3: (b) Construct an 80% confidence interval for the proportion of women who work at home who are college graduates. Round the answer to at least three decimal places. An 80% confidence interval for the proportion of women who work at home who are college graduates is 0.299 < p < 0.355. Part 3 of 3: (c) Based on the confidence interval, is it reasonable to believe that the proportion of college graduates among women who work at home is the same as the proportion of college graduates among men who work at home? Explain.
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Working at home: According to the U.S Census Bureau, 44% of men who worked at home were college graduates. In a sample of 510 women who worked at home, 162 were college graduates. (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is 0.318. (b) Construct a 99% confidence interval for the proportion of women who work at home who are college graduates. Round the answer to at least three decimal places. A 99% confidence interval for the proportion of women who work at home is <p< .
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According to a 2010 report from the American Council on Education, females make up 57% of the college population in the United States. Students in a statistics class at South Texas College want to determine the proportion of female students at STC. They select a random sample of 135 STC students and find that 72 are female, which is a sample proportion of 72/135 ≈ 0.533. So, 53.3% of the students in the sample are female. That is, the sample proportion is 0.533. What can they conclude about the proportion of females at the college? How confident can they be in their estimate? To answer these questions, we need to find the confidence interval to estimate the population proportion. Margin of Error, E = Zα/2√(pq/n) And for the confidence interval, use p ± Margin of Error. Your Task: 1. Find the Margin of Error. 2. Find the confidence interval. Conclusion: We are 95% confident that the proportion of all STC students who are female is between [lower bound] and [upper bound].
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