Let Y1,...,Yn be a random sample from a normal distribution N(μ, o^2), where both the expected value μ and the variance o^2 are unknown parameters. It is customary to estimate patameter o^2 with a sample variance s^2, calculated from the observations y1,...,yn. a. What formula is used to calculate s^2 from observations? b. The distribution result (n-1/o^2)S^2 applies to the corresponding random variable S^2. use this to conduct a test for the null hypothesis H0:0 = σ0 when the counter hypothesis is one-tailed H1: o > σ0. How is the p-value calculated? Here n and o 0>0 are known numbers.
Let Y1,...,Yn be a random sample from a normal distribution N(μ, o^2), where both the expected value μ and the variance o^2 are unknown parameters. It is customary to estimate patameter o^2 with a sample variance s^2, calculated from the observations y1,...,yn. a. What formula is used to calculate s^2 from observations? b. The distribution result (n-1/o^2)S^2 applies to the corresponding random variable S^2. use this to conduct a test for the null hypothesis H0:0 = σ0 when the counter hypothesis is one-tailed H1: o > σ0. How is the p-value calculated? Here n and o 0>0 are known numbers.
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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Transcribed Image Text:Let Y1,...,Yn be a random sample from a normal distribution N(μ, o^2), where both the expected
value μ and the variance o^2 are unknown parameters. It is customary to estimate patameter
o^2 with a sample variance s^2, calculated from the observations y1,...,yn.
a. What formula is used to calculate s^2 from observations?
b. The distribution result (n-1/o^2)S^2 applies to the corresponding random variable S^2.
use this to conduct a test for the null hypothesis H0:0 = 0 when the counter hypothesis
is one-tailed H1: o> 00. How is the p-value calculated? Here n and o 0>0 are known
numbers.
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