Question

7-15. The elastici Creatonalumaris affected 7-15. The elasti. SI Created with ScanWritr. To remove this watermark please use the upgradeptions. 7-29. Data on the oxide thickness of semiconductor wafers are as follows: 425, 431, 416, 420, 421, 436, 418, 410, 431, 433, 423, 426, 411, 435, 436, 428, 411, 426, 407, 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). 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 nanulatained in Scan : Kiswater my hareT 430 options.

Answer 1

> # oxide_thickness of semiconductor wafers are as follows > X <- c(425,431,416,420,421, 436,418,410,431,433,423,426,411,435,436,428, 411,426,40 7,437,422,428,413,416) > # part a) a point estimate of the mean oxide thickness for all wafers in the popu Tation is sample mean > sample_mean <- mean(x) sample_mean [1] 423.3333 > # by mathematical formula > sample_mean <- (1/length(x))*sum(x) > sample_mean [1] 423.3333 > # part b) the point estimate of the standard deviation of oxide thickness for all wafers in the population is sample standard deviation > sample_standard_deviation <- sd(x) > sample_standard_deviation [1] 9.149325 > # by mathematical formula > sqrt((1/(length(x)-1))*sum((x-mean(x))^2)) [1] 9.149325 > # part c) the standard error of the point estimate from the sample mean is > standard_error <- sqrt((1/(length(x)-1)) *sum((x-sample mean)^2))/sqrt(length(x)) > standard_error [1] 1.867598 > # by another formula > sd(x)/sqrt(length(x)) [1] 1.867598 > # part d) sample median is the point estimate of population median > sample_median <- median(x) > sample_median [1] 424