Suppose that X₁, X₂,Xn and Y₁, Y2, .Yn are independentrandom samples from populations with means ₁ and ₂ and variances of and o2,respectively. Show that X - Y is a consistent estimator of μ₁ - 2.

Let X=X1,X2,..,Xn and Y=Y1,Y2,...,Yn are independent random samples from a population.Here, μ1 and…

Answered: Suppose that X₁, X2, . . ., X₁ and Y₁,…

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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A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 14 using fertilizer A and 19 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results are below. Is there evidence of a significant difference between the tomato yields based on the fertilizer brand? Fertilizer Fertilizer B Average number of tomatoes per plant 18.4 19.1 Standard deviation 3.2 4.7 Number of plants 19 14
12. The OLS estimators of the coefficients in a multivariate linear regression model will be unbiased and consistent if the following set of conditions holds A. expected value of the error term given the independent variables is zero, the variance of the error term does not depend on the values of the independent variables, the observations (Yi,Xi,1,X₁,2,...,Xik) are i.i.d., large outliers are unlikely B. expected value of the error term given the independent variables is zero, the variance of the error term does not depend on the values of the independent variables, there is no perfect multicollinearity between the independent variables, the observations (Y₁X₁,1X₁,2,...,Xik) are i.i.d. C. expected value of the error term given the independent variables is zero, there is no perfect multicollinearity between the independent variables, the observations (Yi,Xi,1,Xi,2,...,Xik) are i.i.d., large outliers are unlikely D. the variance of the error term does not depend on the values of the…
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ2. The null and alternative hypotheses are Ho: μ₁ −μ₂ ≤0 and H₁ : µ₁ −µ₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. a. Can you reject the null hypothesis, using a probability of Type I error α = 0.05, if the sample standard deviation from process 1 is 28 and from process 2 is 23? (Round to three decimal places as needed.) The test statistic is t =
A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3 78.5 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic = p-value = The p-value is The correct…
A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below [L] or above [H]. Find L and H values. Options listed below. [L] answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92. [H] Answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92.
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Suppose that X₁, X2, . . ., X₁ and Y₁, Y₂ , . . Yn are independent . random samples from populations with means µ₁ and µ₂ and variances o² and o² respectively. Show that X - Y is a consistent estimator of μ₁ − μ₂.