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7.3.7 WP SS VS Data on the oxide thickness of semicon- ductor wafers are as follows: 425, 431, 416, 419, 421, 436, 418, 410, 431, 433, 423, 426, 410, 435, 436, 428, 411, 426, 409, 437, 422, 428, 413, 416. a. Calculate a point estimate of the mean oxide thickness for all wafers in the population. b. Calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population. c. Calculate the standard error of the point estimate from part (a). d. Calculate a point estimate of the median oxide thickness for all wafers in the population. e. Calculate a point estimate of the proportion of wafers in the population that have oxide thickness of more than 430 angstroms. 7.3.8 Suppose that X is the number of observed "successes” in a sample of n observations where p is the probability of success on each observation. a. Show that P = X/n is an unbiased estimator of p. b. Show that the standard error of ê is √/p(1 − p)/n. How would you estimate the standard error? 7.3.9 VS X, and S² are the sample mean and sample variance from a population with mean µ₁ and variance 62 7. Similarly, X2 and Sare the sample mean and sample variance from a second inde- pendent population with mean µ and variance σ22. The sample sizes are n₁ and n₂, respectively. a. Show that X₁ - X2 is an unbiased estimator of μ₁ - μ2. b. Find the standard error of ✗₁ - X2. How could you estimate the standard error? c. Suppose that both populations have the same variance; that is, σ² = 62 = 0². Show that (n₁ − 1) S² + (n − 1) S22 is an unbiased estimator of σ². +12-2

7.3.7 WP SS VS Data on the oxide thickness of semicon- ductor wafers are as follows: 425, 431, 416, 419, 421, 436, 418, 410, 431, 433, 423, 426, 410, 435, 436, 428, 411, 426, 409, 437, 422, 428, 413, 416. a. Calculate a point estimate of the mean oxide thickness for all wafers in the population. b. Calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population. c. Calculate the standard error of the point estimate from part (a). d. Calculate a point estimate of the median oxide thickness for all wafers in the population. e. Calculate a point estimate of the proportion of wafers in the population that have oxide thickness of more than 430 angstroms. 7.3.8 Suppose that X is the number of observed "successes” in a sample of n observations where p is the probability of success on each observation. a. Show that P = X/n is an unbiased estimator of p. b. Show that the standard error of ê is √/p(1 − p)/n. How would you estimate the standard error? 7.3.9 VS X, and S² are the sample mean and sample variance from a population with mean µ₁ and variance 62 7. Similarly, X2 and Sare the sample mean and sample variance from a second inde- pendent population with mean µ and variance σ22. The sample sizes are n₁ and n₂, respectively. a. Show that X₁ - X2 is an unbiased estimator of μ₁ - μ2. b. Find the standard error of ✗₁ - X2. How could you estimate the standard error? c. Suppose that both populations have the same variance; that is, σ² = 62 = 0². Show that (n₁ − 1) S² + (n − 1) S22 is an unbiased estimator of σ². +12-2

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter29: Tolerance, Clearance, And Interference
Section: Chapter Questions
Problem 18A: A piece is to be cut to the dimensions and tolerances shown in Figure 29-14. Determine the maximum...
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Answer questions 7.3.7, 7.3.8 and 7.3.9 respectively with detailed solutions please 

7.3.7 WP SS VS Data on the oxide thickness of semicon- ductor wafers are as follows: 425, 431, 416, 419, 421, 436, 418, 410, 431, 433, 423, 426, 410, 435, 436, 428, 411, 426, 409, 437, 422, 428, 413, 416. a. Calculate a point estimate of the mean oxide thickness for all wafers in the population. b. Calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population. c. Calculate the standard error of the point estimate from part (a). d. Calculate a point estimate of the median oxide thickness for all wafers in the population. e. Calculate a point estimate of the proportion of wafers in the population that have oxide thickness of more than 430 angstroms. 7.3.8 Suppose that X is the number of observed "successes” in a sample of n observations where p is the probability of success on each observation. a. Show that P = X/n is an unbiased estimator of p. b. Show that the standard error of ê is √/p(1 − p)/n. How would you estimate the standard error? 7.3.9 VS X, and S² are the sample mean and sample variance from a population with mean µ₁ and variance 62 7. Similarly, X2 and Sare the sample mean and sample variance from a second inde- pendent population with mean µ and variance σ22. The sample sizes are n₁ and n₂, respectively. a. Show that X₁ - X2 is an unbiased estimator of μ₁ - μ2. b. Find the standard error of ✗₁ - X2. How could you estimate the standard error? c. Suppose that both populations have the same variance; that is, σ² = 62 = 0². Show that (n₁ − 1) S² + (n − 1) S22 is an unbiased estimator of σ². +12-2
Transcribed Image Text:7.3.7 WP SS VS Data on the oxide thickness of semicon- ductor wafers are as follows: 425, 431, 416, 419, 421, 436, 418, 410, 431, 433, 423, 426, 410, 435, 436, 428, 411, 426, 409, 437, 422, 428, 413, 416. a. Calculate a point estimate of the mean oxide thickness for all wafers in the population. b. Calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population. c. Calculate the standard error of the point estimate from part (a). d. Calculate a point estimate of the median oxide thickness for all wafers in the population. e. Calculate a point estimate of the proportion of wafers in the population that have oxide thickness of more than 430 angstroms. 7.3.8 Suppose that X is the number of observed "successes” in a sample of n observations where p is the probability of success on each observation. a. Show that P = X/n is an unbiased estimator of p. b. Show that the standard error of ê is √/p(1 − p)/n. How would you estimate the standard error? 7.3.9 VS X, and S² are the sample mean and sample variance from a population with mean µ₁ and variance 62 7. Similarly, X2 and Sare the sample mean and sample variance from a second inde- pendent population with mean µ and variance σ22. The sample sizes are n₁ and n₂, respectively. a. Show that X₁ - X2 is an unbiased estimator of μ₁ - μ2. b. Find the standard error of ✗₁ - X2. How could you estimate the standard error? c. Suppose that both populations have the same variance; that is, σ² = 62 = 0². Show that (n₁ − 1) S² + (n − 1) S22 is an unbiased estimator of σ². +12-2
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