题目
题目

X_405078 Short practice quiz

多重下拉选择题

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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