Unformatted text preview: 5%: Suppose that X has a discrete uniform distribution 1/3! I = 13 25 3
0, otherwise xxx) x {
Crdom sample of n = 36 is selected from this population.
lithe probability that the sample mean is greater than 2.1 7—15. Let X1,)13,,X7 denote a random sample from a population having mean .11. and variance 0'2. Consider the
following estimators of 11.: A XVI+X2+“'+X7
®l:_'—"——7"———— 2X1“X6+X4
2 @2: (a) Is either estimator unbiased? (b) Which estimator is best? In what sense is it best?
Calculate the relative efficiency of the two estimators. 7 22. Data on pull oﬁ'" force (pounds) for connectors used';
an automobile engine application are as follows: 79.3, 75.1,
78.,2 74.1, 73,9 75.,0 77.6, 77.3, 73.8, 74.,6 75.,5 74.,0 74"
75.9, 72. 9, 73 8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9,13'
75.1, 76.8. '
(a) Calculate a point estimate of the mean pulloff force of :1”: connectors in the population. State which estimator 1.;
used and why. (b) Calculate a point estimate of the pull off force value .3
separates the Weakest 50% of the connectors in the pop
lation from the strongest 50%. . (c) Calculate point estimates of the population variance :1}
the population standard deviation. (d) Calculate the standard error of the point estimate found m
part (a). Provide an interpretation of the standard er 11”. (e) Calculate a point estimate of the proportion of all connect
in the population whose pulloff force is less than 73 poun "an. _ ...
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 Spring '10
 Zhai

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