65. Suppose that a random sample of size 20 is taken from a normal distributionwith unknown mean and known variance equal to 1, and the mean is found tobe x = 10, A normal distribution was used as the prior for the mean, and it wasfound that the posterior mean was 15 and the posterior standard deviation wa:s0.1. What were the mean and standard deviation of the prior?

Given sample size n = 20variance = σ2 = 1Poterioir mean = µpost = 15Posterioir Standard deviation =…

Answered: 65. Suppose that a random sample of…

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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An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
Consider a population that has a score of X = 15 associated with a z-score of +1.50. What does this z-score indicate about the location of X = 15? A score of X = 15 is 1.5 mean units below the standard deviation. A score of X = 15 is 1.5 mean units above the standard deviation. A score of X = 15 is 1.5 standard deviations above the mean. A score of X = 15 is 1.5 standard deviations below the mean.
Suppose you are working with a data set that is normally distributed, with a mean of 250 and a standard deviation of 46. Determine the value of x from the following information. (d) x is greater than 57% of the values
We want to estimate mean of a distribution by taking i.i.d. measurements, and computing their sample mean. Suppose we might be able to improve the precision of the measurements by refining the experiments, meaning we might be able to reduce the variance of the measurements (up to a point). Assuming we want to estimate the mean by conducting exactly 100 experiments, with an error of at most 1 unit and 99% certainty, how low should the variance be (approximately)?
Suppose the mean and standard deviation of the GPAs at school are Xbar = 1.487; and s = 1.332Claire's GPA has a z-score of -2.320. What is Claire's GPA?(Leave your answer to 2 decimals: ex: 1.23)
For a population with mean of 50 and a standard deviation of 8, what is the z-score that corresponds to X-58? а. 1.5 b. -0.5 C. 1 d. -2 е. 2.5
. If X is a normally distributed random variable with a mean of 235 Findthe standard deviation given ?(? > 250) = 0.37 . Sketch the graph.
Suppose the scores of students on an exam are Normally distributed with a mean of 522 and a standard deviation of 83. Then approximately 99.7% of the exam scores lie between the numbers such that the mean is halfway between these two integers. and ☐
Which of the following samples would have the largest standard error of the mean? It's not possible to tell n = 32 scores from a population with σ = 10 n = 89 scores from a population with σ = 20 n = 88 scores from a population with σ = 10 n =18 scores from a population with σ = 20
Suppose the mean and standard deviation of the GPAs at Tulane are Xbar = 2.899; and s = -0.753Charlie's GPA has a z-score of -0.140. What is Charlie's GPA?(Leave your answer to 2 decimals: ex: 1.23)
Do the mean weights of male college freshmen and male college seniors differ? There are arguments for and against this question. The mean weight, μx of college freshmen will be compared to the mean weight, My of college seniors. The true values of Mx and My are unknown. It is recognized that the true standard deviations are x = 13 for male college freshmen and dy = 24 for male college seniors. We take a random sample of m = 431 college freshmen and a random sample of n=289 college seniors. The mean weights were x = 178 for male college freshmen and y = 185 for male college seniors. Assuming independence between the samples and assuming the weights are normally distributed we would like to estimate My - My. a) What is the standard deviation of the distribution of x?[ b) What is the standard deviation of the distribution of x-y? c) Create a 95% confidence interval for Mx - Hy? d) What is the length of the confidence interval in part c) ? e) If we let n stay at 289 but vary m, what is the…
6. For a distribution of scores, X = 40 corresponds to a z-score ofz = +1.00, and X = 28 corresponds to a z-score of z =- 0.50. What are the values for the mean and standard deviation for the distribution?

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