HW_chapter7 - 5 Suppose that X has a discrete uniform...

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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 pull-off 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 1-1”. (e) Calculate a point estimate of the proportion of all connect in the population whose pull-off force is less than 73 poun "an. _ ...
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