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X_405078 Short practice quiz

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Birthweights a) The vector birthweight contains the birthweights (in grams) of 188 newborn babies. Denote the underlying mean birthweight by μ. Suppose we implemented the following commands in R: > mean(birthweight) 2913.293 > var(birthweight) 486506.6 > qnorm(0.96) 1.750686 > qnorm(0.98) 2.053749 > qnorm(0.975) 1.959964 > qnorm(0.985) 2.17009 > qnorm(0.99) 2.326348 Assuming normality, construct a bounded 98% confidence interval (CI) for μ: [ Select ] [2802.05, 3024.53] [2812.94, 3013.65] [2793.93, 3032.66] [2788.40, 3038.18] . Evaluate the sample size needed to provide that the length of the 97%-CI is at most 100: [ Select ] . Would it be possible to compute a bootstrap 95%-CI for μ by using the sample birthweights? [ Select ] no yes not relevant .

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We begin by parsing the problem: you have a vector of birthweights with n = 188, sample mean around 2913.293 g and sample variance about 486,506.6, suggesting a substantial spread. The task is to (i) identify the 98% CI for μ under normality, (ii) determine the sample size needed so the 97% CI length is at most 100, and (iii) judge whether a bootstrap 95% CI for μ using the observed data is possible. Option A for the first dropdown: [2793.93, 3032.66] - To form a 98% CI for μ using the normal approximation, we use mean ± z_{0.99} * (s/√n). Here s is the sample standard deviation, s = sqrt(486506.6) ≈ 697.5, and √n = sqrt(188) ≈ 13.71, giving SE ≈ 697.5 / 13.71 ≈ 50.9. - The 98% z-critical value is z_{0.99} ≈ 2.3263. The margin of error is 2.3263 * 50.9 ≈ 118.3. - The......Login to view full explanation

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