Suppose that xi and x2 are random samples of observations from a population with mean m and variances2. Consider the following three point estimators, A.B.C, of m:*1 + x2*1 + 3r2*1 + 2x2C =A =B =23a) Which of these estimators yields an unbiased estimator of m? Justify your answer.b) Of those that are unbiased, which is the most efficient? Justify your answer.

Given Information: Mean of x1 and x2=mvariance of x1 and x2=s2No. of point estimators=03…

Answered: Suppose that xi and x2 are random…

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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The relatively efficient estimator has the variance. ...... .............. O a. maximum O b. least O c highest O d. atmost O e. None of these.
Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market if the new trash bag's mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 39 trash bag breaking strengths in Table 1.10 is x = 50.573. If we let u denote the mean of the breaking strengths of all possible trash bags of the new type and assume that o equals 1.61: Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 50 pounds?
Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?. 302 Which of the estimators have a variance of 2 X1+X2++X7 7 2X1-X6+X4 3X1-X3+X4 2 2(X1+X2+…+X7) 4 7
Let X denote the sample average for a random sample with mean uu and variance 02. Consider the following estimator for u: W=n+2/n+1°X Is W as consistent estimator of u? a. Yes b. No c. It depends
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Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7
Let Y1 and Y2 be independent random variables with unknown mean μ and known variance σ2 =1. Which of the following two estimators of μ has smaller MSE? Justify your answer.
answer the second question.
Let X, and X, be independent random variables with mean u and variance o?. Suppose that we have two estimators of u: 3X, -X, and 9,* ,then the variance of each estimator is 3 2
3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be two estimates of u. * Which of these two estimators is unbiased? * Which is the better estimator, and why? %3D
9
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance ?2 = 42.3. In a different section of Chaco Canyon, a random sample of 19 transects gave a sample variance s2 = 46.9 for the number of sites per transect. Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3. Find a 95% confidence interval for the population variance. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)- 19.96 What are the degrees of freedom? -18 (c) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005…

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