Suppose we observe two independent random samples X1,..., X, with each X; ~ N(u1, 0²) and Y1,...,Yng with each Y; ~ N(42, o²).We will assume that µ1, #2 and o² are unknown.We are given z = 10.1, ỹ = 7.1, s = 5.5 and s? = 6.4, with ny = 13 and ng = 19.Suppose we want to formally test the assumption tha: the variances of the the two populations the samples come from are equal. What is thetest statistic we should use?Select one:O a. W("1 1)53%3D2~6.4O b. F%3DO c. W(n-1)s2.5.5We will now compute a 95% contidence interval tor the ratio ot . Here, we are no longer assuming equal variances, so o denotes thepopulation variance of each X; and of denotes the population variance of each Y;.What is the lower endpoint of this confidence interval? Give answer to 3 decimal places.What is the upper endpoint of this confidence interval?

We want to find 95% CI for ratio of population variances

Answered: Suppose we observe two independent…

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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If you let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assuming the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4 and you test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi, what would be the critical region for an alpha = 0.05 significance level?
2.Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.1, 9.9, 10.2, 10.3, 10.3, 9.7, 9.8, 10.5, 10.2, and 9.8 liters. Use alpha 0.01 and assume that the distribution of content is normal.
Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
Let X1,...,Xn be an iid sample from f(x | θ) = θxθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
Suppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the constant a ?
Find the sampling distributions of Y1 and Yn for ran-dom samples of size n from a population having the beta distribution with α = 3 and β = 2.
To test Upper H 0: mu equals 60 versus Upper H 1: mu less than60, a random sample of size N equals 25 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.
Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
To test H0: μ=50 versus H1: μ<50, a random sample of size n=23 is obtained from a population that is known to be normally distributed. If x=46.6 and s=11.8, compute the test statistic.
A simple random sample of size 200 is taken from a much larger group of male wrestlers prior to a competition. The average weight in the sample is 190 pounds, with an SD of 20 pounds. The average weight of the population is estimated to be 190 pounds, and this estimate is likely to be off by about _______.
Let the following simple random sample following:1. Binomial pmf. (11, ¾);2. Uniform pmf;3. Uniform pdf (0, a);4. Exponential pdf with (µ) .Find the corresponding pmf/pdf of Y1 , Y4 , Y7 and F(Yi) where

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