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,., Yn. Suppose that the X;'s constitute a random sample from a distribution with mean u1 and standard deviation o1 and that the Y,'s form a random sample (independent of the X's) from another distribution with mean la and standard

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2. 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, ..., Yn. Suppose that the X;'s constitute a random sample from a distribution
with mean µ1 and standard deviation ơ1 and that the Y;'s form a random sample
(independent of the X;'s) from another distribution with mean µ2 and standard
deviation ơ2.
(a) Use rules of expected value to show that X
µ1 – H2. Calculate the estimate for the given data.
Y is an unbiased estimator of
(b) Use rules of variance to obtain an expression for the variance and standard
deviation (standard error) of the estimator in part (a), and then compute the
estimated standard 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 se-
lected. Calculate a point estimate of the variance of the difference X – Y
between male and female IQ.
Transcribed Image Text:2. 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, ..., Yn. Suppose that the X;'s constitute a random sample from a distribution with mean µ1 and standard deviation ơ1 and that the Y;'s form a random sample (independent of the X;'s) from another distribution with mean µ2 and standard deviation ơ2. (a) Use rules of expected value to show that X µ1 – H2. Calculate the estimate for the given data. Y is an unbiased estimator of (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated standard 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 se- lected. Calculate a point estimate of the variance of the difference X – Y between male and female IQ.
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