Let X₁,..., Xn each be independently distributed N(µ, σ²) where o = 3.0. Suppose the sample mean isX = = Xi= 58.3n i=1File Preview(a) Compute a 95% and a 99% CI for µ when n= 25.(b) Compute a 95% and a 99% CI for μ when n=10.Now assume that o is unknown and gets estimated by the sample SD s = 4.3.(c) Compute a 95% and a 99% CI for μ when n = 25.(d) Compute a 95% and a 99% CI for u when n = 10.Compare your answers for fixed n, and fixed confidence level, respectively. In addition, would the confi-dence interval get larger or smaller if o is unknown for fixed sample size and confidence level? Explainwhy.

Given, σ=3.0, and x¯=58.3 We need to compute the confidence interval for mean. Note that since you…

Answered: Let X₁,..., Xn each be independently…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For mated pairs of gallinules (type of water bird), let X equal the weight in grams of the male and Y the weight in grams of the female. Assume that X and Y have a bivariate normal distribution with #x = 415, o = 611, y = 347 and o=689. The correlation coefficient between X and Y is p = -0.25. (b) Determine the marginal distributions of X and then of Y. (c) Find the conditional distribution of Y|X = x. (d) Find E(Y|X = z) and Var(Y|X = x).
A professor grades on a curve by assigning C's to all scores from u- ; to u+%, B's to all scores from i+% to µ+ , and D's to all scores from u – * to µ – 5. Everyone who scores below a D gets an F, and everyone who scores above a B gets an A. a. If the scores are normally distributed with mean u and variance o², what percentage of students will receive each grade? Hint: convert to z-scores and use pnorm() to find probabilities (percentages) b. If the scores are uniformly distributed (continuous) from 0 to 100 what percentage will receive each grade? Hint: first determine the values of u and o for this distribution
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26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.37 0.75 0.60 0.49 2.66 1.18 0.33 0.46 0.46 1.64 0.33 0.50 0.58 0.41 1.39 (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N, is ____ and the degrees of freedom for the denominator, d.f.D, is _____ The critical…
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