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4. The data set mentioned in Exercise 1 also includes these third grade verbal IQ observations for males: 117 103 121 112 120 132 113 117 132 149 125 131 136 107 108 113 136 114 and females 114 102 113 131 124 117 120 90 114 109 102 114 127 127 103 Prior to obtaining data, denote the male values by X1, ..., Xm and the female values by Y, .. ., Yµ. Suppose that the X;'s constitute a random sample from a distribution with mean u, and standard deviation o 1 and that the Y's form a random sample (independent of the X;'s) from another distribution with mean 42 and standard deviation o2. a. Use rules of expected value to show that X – Y is an unbiased estimator of µ1 – 42. Calculate the estimate for the given data. b. Use rules of variance from Chapter 6 to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated stan- dard error. c. Calculate a point estimate of the ratio o1/02 of the two standard deviations. d. Suppose one male third-grader and one female third-grader are randomly selected. Calculate a point estimate of the variance of the difference X – Y between male and female IQ.

4. The data set mentioned in Exercise 1 also includes these third grade verbal IQ observations for males: 117 103 121 112 120 132 113 117 132 149 125 131 136 107 108 113 136 114 and females 114 102 113 131 124 117 120 90 114 109 102 114 127 127 103 Prior to obtaining data, denote the male values by X1, ..., Xm and the female values by Y, .. ., Yµ. Suppose that the X;'s constitute a random sample from a distribution with mean u, and standard deviation o 1 and that the Y's form a random sample (independent of the X;'s) from another distribution with mean 42 and standard deviation o2. a. Use rules of expected value to show that X – Y is an unbiased estimator of µ1 – 42. Calculate the estimate for the given data. b. Use rules of variance from Chapter 6 to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated stan- dard error. c. Calculate a point estimate of the ratio o1/02 of the two standard deviations. d. Suppose one male third-grader and one female third-grader are randomly selected. Calculate a point estimate of the variance of the difference X – Y between male and female IQ.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Could you solve part d please.

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PROPOSITION Let X1, X2, ..., X, have mean values µ1, ..., Un, respectively, and variances of,..., o, respectively. 1. Whether or not the X;'s are independent, E(a,X1 +...+ a„X„) = a¡E(X1)+·… + a„E(X„) (6.7) = ajli +. +anfln 2. If X1, ..., , Xn are independent, V(a,X1 +..+ anX„) = a¡V(X1)+ ...+aV(X„) (6.8) = ajo;+ + a,, and Važoj + · · ·+ azo? (6.9) 3. For any X1, X2, . . ., Xn, n V(αι Χ + .+ α,X.) -ΣΣααcov (X, X) (6.10) i=1 j=1
Transcribed Image Text:PROPOSITION Let X1, X2, ..., X, have mean values µ1, ..., Un, respectively, and variances of,..., o, respectively. 1. Whether or not the X;'s are independent, E(a,X1 +...+ a„X„) = a¡E(X1)+·… + a„E(X„) (6.7) = ajli +. +anfln 2. If X1, ..., , Xn are independent, V(a,X1 +..+ anX„) = a¡V(X1)+ ...+aV(X„) (6.8) = ajo;+ + a,, and Važoj + · · ·+ azo? (6.9) 3. For any X1, X2, . . ., Xn, n V(αι Χ + .+ α,X.) -ΣΣααcov (X, X) (6.10) i=1 j=1
4. The data set mentioned in Exercise 1 also includes these third grade verbal IQ observations for males: 117 103 121 112 120 132 113 117 132 149 125 131 136 107 108 113 136 114 and females 114 102 113 131 124 117 120 90 114 109 102 114 127 127 103 Prior to obtaining data, denote the male values by X1, ..., Xm and the female values by Y1, .. ., Y.. Suppose that the X;'s constitute a random sample from a distribution with mean u1 and standard deviation o and that the Y;'s fom a random sample (independent of the X;'s) from another distribution with mean µ2 and standard deviation o2. a. Use rules of expected value to show that X – Y is an unbiased estimator of µ1 – µ2. Calculate the estimate for the given data. b. Use rules of variance from Chapter 6 to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated stan- dard error. c. Calculate a point estimate of the ratio o1/02 of the two standard deviations. d. Suppose one male third-grader and one female third-grader are randomly selected. Calculate a point estimate of the variance of the difference X – Y between male and female IQ.
Transcribed Image Text:4. The data set mentioned in Exercise 1 also includes these third grade verbal IQ observations for males: 117 103 121 112 120 132 113 117 132 149 125 131 136 107 108 113 136 114 and females 114 102 113 131 124 117 120 90 114 109 102 114 127 127 103 Prior to obtaining data, denote the male values by X1, ..., Xm and the female values by Y1, .. ., Y.. Suppose that the X;'s constitute a random sample from a distribution with mean u1 and standard deviation o and that the Y;'s fom a random sample (independent of the X;'s) from another distribution with mean µ2 and standard deviation o2. a. Use rules of expected value to show that X – Y is an unbiased estimator of µ1 – µ2. Calculate the estimate for the given data. b. Use rules of variance from Chapter 6 to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated stan- dard error. c. Calculate a point estimate of the ratio o1/02 of the two standard deviations. d. Suppose one male third-grader and one female third-grader are randomly selected. Calculate a point estimate of the variance of the difference X – Y between male and female IQ.
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