Example 17-8. X1, X2, and X3 is a random sample of size 3 from a population with meanvalue u and variance ơ². T,, T2, T3 are the estimators used to estimate mean value µ, where11T1= X1 + X2 – X3, T2= 2X1+3X3– 4X2 ,T3 =} (^X,+ X2 + X3)/3.and|(i) Are T1 and T2 unbiased estimators ?(ii) Find the value of A such that T3 is unbiased estimator for u.(iii) With this value of A is T3 a consistent estimator ?(iv) Which is the best estimator ?

Answered: Image /qna-images/answer/51156d30-8a91-4a53-be99-f7ffe27e515e.jpg

Answered: Example 17-8. X1, X2, and X3 is a…

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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Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: �"!= 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4.What is the variance of � "!
A researcher investigates whether cold medication effects mental alertness. It is known that scores on a standardized test containing a variety of problem-solving tasks are normally distributed with  = 64 and  = 8. A random sample of n = 16 teenage and a sample of n = 25 adults are given the drug and then tested. On average, the teenagers scored and average of ? = 58 and the adults scored and average of M = 65.5.a. Are the data sufficient to conclude that the medication significantly reduces mental alertness in teenagers? Test with  = .01.b. Are the data sufficient to conclude that the medication significantly increases mental alertness in adults? Test with  = .01.
1. Six batteries taken at random from a large lot were subjected to life tests with the following results: 19, 22, 18, 16, 25, and 20 hours. Find the probability that the sample mean of x= 20 hours, as observed here, or one less than 20 hours could arise if the true mean of the lot of batteries is 21.5 hours, assuming a known variance of o = 10 hours, for the individual batteries in the lot. %3D
Suppose that having a widow's peak was a dominant trait (W) compared to not having a widow's peak (w). In a sample size of 30 students, 15 were observed to have a widow's peak and 15 did not have a widow's peak. The expected frequency of a widow's peak is 75% chance of getting it and a 25% chance of not getting it. Perform a chi square analysis to see if the data above agrees with the predicted outcome.
Consider a regression analysis with n= 51 and four potential independent variables. Suppose that one of the independent variables has a correlation of 0.49 with the dependent variable. Does this imply that this independent variable will have a very small Student's t statistic in the regression analysis with all four predictor variables? Choose all that apply. A. The correlation between the independent variable and the dependent variable could result in a very small Student's t statistic as the correlation creates a high variance. B. Correlation between the independent variable and the dependent variable is not necessarily evidence of a small Student's t statistic. C. A high correlation among the independent variables could result in a very small Student's t statistic as the correlation increases the coefficient standard errors. D. Correlation between the independent variable and the dependent variable is evidence of a small Student's t statistic.
How do you find the mean and variance of part(d)?I need the detailed solution.
18. A set of n = 52 pairs of scores (X and Y values) in a research study has a Pearson correlation of r = -0.7. What percentage of the variance for the Y scores is predicted by its relationship with X?
Suppose that we would like to test the following hypotheses on the population correlation coefficient ρ: H0: ρ ≤ 0 and H1: ρ > 0. The sample correlation coefficient (r) for a sample with 7 observations (n = 7) on x and y is 0.35 . Then the test statistic t has a value of

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