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 i = 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 was0.1. What were the mean and standard deviation of the prior?

The prior Standard deviation is obtained below:

Answered: Suppose that a random sample of size 20…

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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State whether the following statements are true or false : (i) For any data, larger the mean larger is the standard deviation. (ii) If every item of a distribution of 10 values is 35, then standard deviation is 1. (iii) Standard deviation can be defined as the mean of the square root of the sum of squared deviations about the mean. (iv) The variance of 10 observations is 4, their S.D. is + 2 or - 2.
(a) Compute a 95% CI for u (b) Compute a 99% CI for µ. (c) Which of the two intervals has bigger length, and why?
A researcher hypothesizes that the SUNY professors have a higher job satisfaction level than the population average. Suppose it is known that the population mean of the overall job satisfaction is 28. Use the data presented in the previous question to test the researcher's hypothesis at a 0.05 significant level. List four steps
Suppose the length of a particular type of snake is normally distributed with a mean of 50 inches and a standard deviation of 2.2 inches. You took a sample of 25 such snakes and the mean length for these snakes is 53 inches. a. Test the hypothesis that this sample came from a population with an average length of 50 inches. What is your conclusion if α = .05. Show your calculations including Excel functions used to do the calculations. b. Your friend believes that you took the sample from a population of snakes whose length is below 50 inches. Is your friend correct? What is your conclusion? Use α = .05 (5+5)
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A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean ? = 82 and standard deviation ? = 22. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 125 (borderline diabetes starts at 125)
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Mason earned a score of 226 on Exam A that had a mean of 250 and a standard deviation of 40. He is about to take Exam B that has a mean of 550 and a standard deviation of 25. How well must Mason score on Exam B in order to do equivalently well as he did on Exam A? Assume that scores on each exam are normally distributed.
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean ? = 81 and standard deviation ? = 26. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 125 (borderline diabetes starts at 125)
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