Solve both parts 3 and 4 of the question below. Let Y1, Y2, Y3,Yn* N(u, 02), where o?25 is known.....3. Suppose we collect data of size n = 16 and the MLE turns out to be îu = 2 and ô² = 25.Using the result from the previous part, conduct an a = .05 level test of Ho : µ = 0in favor of Ha : µ #0. Find the critical value, rejection region, and p-value. Interpretthe p-value. Do you reject or fail to reject the null?4. Invert the a-level test you found in the previous part to construct a 95% confidenceinterval for u. Interpret the confidence interval.

Given: Population variance σ2 = 25 Population standard deviation σ = 5 Sample size n = 16 Sample…

Answered: iid Let Y1, Y2, Y3, . .., Y, N(µ, o²),…

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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Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that thee is a difference in pupil sizes between males and females, using an alpha level of .01. Males Females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.7 7.9 6.9 8.8 4.5 9.0 7.5 9.0 What is the Critical Value?
In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school, 70% were enrolled in college. At α=0.07, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Find the critical value(s) and identify the rejection region(s).
Let X1,...,Xn be iid exponential(θ) random variables. Derive the LRT of H0 : θ = θ0 versus Ha : θ 6= θ0. Determine an approximate critical value for a size-α test using the large sample approximation.
From exercise 9-15 Find the boundary of the critical region if the type I error probability is a) alpha = 0.01 and n = 10 b) alpha = 0.05 and n=10 c) alpha = 0.01 and n=16 d) alpha = 0.05 and n=16 From exercise 9-15 standard deviation = 20 H0: mu = 175 H1: mu >175
Let X 1 ,X 2 ,...,X n be a r.s. of size n from a distribution N(theta, 1) find best critical region of size a for testing H 0 : theta=0 against H 1 : theta=1 , also find the value of c if n = 25 and a = 5%.
If I have a sample mean less than 30 at alpha= 0.05. What is the critical value using the Z table
Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size nfrom a distribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere. Show that thekth order statistic Yk has a beta pdf with parameters α = k and β = n − k + 1.
A researcher is interested in testing whether annual house hold income in Philadelphia is normal. So she took a sample of 50 house holds and found that skewness (s)= 2.3190 and Kurtosis (k) = 6.7322. Use the Jarque- Bera Test to test , at alpha 0.05, whether income follows normal distribution. -Yes, population is normal because Chi-Square test is higher than critical value. -Yes, population is normal because Chi-Square test is less than critical value. -No, population is not normal because Chi-Square test is higher than critical value. -No, population is not normal because Chi-Square test is less than critical value.
A civil engineer is studying the live loads on a highway bridge. Let Y and Z denote the live load (in ten thousands of pounds) for traffic going east and west, respectively, at a randomly selected time of day. Suppose these random variables have a joint distribution with density function f(y,z) = (1/400)yz2e–y/5–z/2, for y > 0, z > 0. If the loads are in opposite directions independent, what should the correlation coefficient and the regression curve of Y on Z be?
What is the critical value? Wj\hat is the p value?
The joint PDF of the random variables X and Y is constant on the region (x,y):x≥0∩yleq1∩−0.5≤x−y≤0, shown in the image below, and is zero outside. Determine P(Y>0.5|X<0.5)
Do one of the following, as appropriate: (a) Find the critical value Za/2, (b) find the critical value t₁/2, (c) state that neither the normal nor the t distribution applies. 90%; n = 10; o is unknown; population appears to be normally distributed za/2=1.383 ta/2=1.812 za/2=2.262 ta/2=1.833

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