ISYE 3770 Fall 2021 Statistics & Applications HW #6 (due on Friday, November 12, 11:59 pm ET) { = Problem 1 (Modified fr

[answerhappygod]

Isye 3770 Fall 2021 Statistics Applications Hw 6 Due On Friday November 12 11 59 Pm Et Problem 1 Modified Fr 1 (110.51 KiB) Viewed 92 times

ISYE 3770 Fall 2021 Statistics & Applications HW #6 (due on Friday, November 12, 11:59 pm ET) { = Problem 1 (Modified from Problem 7-10 on page 248). Suppose that the random variable X has the continuous uniform distribution 1, 05:31 0, otherwise Suppose that a random sample of n = 12 observations is selected from this distribution, and consider the sample mean X. Although the sample size n = 12 is not big, we assume that the Central Limit Theorem is applicable. (a) What is the approximate probability distribution of X? Find the mean and variance of this quantity. (b) Find the probability that the sample mean is greater than 0.45, but less than 0.65. That is, use Appendix Table III on page 743 of our text to approximate the probability P(0.45 < X < 0.65). (e) Find the value c so that the sample mean is greater than 0.5 – c, but less than 0.5 + c with apprxoimately probability 0.95. That is, find c so that P(0.5-c< X <0.5+c) 0.95. 2 Problem 2 (Modified from Problem 7-24 on page 255). Let X, and X, be independent random variables with mean y and variance o?. Suppose that we have three estimators of : 6, X1 + X2 02 X+3X2 X1 + X2 and og (a) What is the bias of each estimator when estimating ? (b) What is the variance of each estimator? (c) What is the mean squared error (MSE) of each estimator? (a) Among these three estimators, which estimator should never be used in term of larger MSE)? Why? Problem 3 (Problem 7-34 on page 255). Data on pull-off force (pounds) for connectors used in 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, 74.7, 75.9, 72.9, 73.8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9, 78.0, 75.1, 76.8. (a) Calculate a point estimate of the mean pull-force of all connectors in the population. State which estimator you used and why. (b) Calculate a point estimate of the pull-force value that separate the weakest 50% of the connectors in the population from the strongest 50%. (c) Calculate point estimates of the population variance and the population standard deviation. (d) Calculate the standard error of the point estimate found in part (a). Provide an interpretation of the standard error. (e) Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds.