A normally distributed quality characteristic is monitored with a moving average (MA)control chart. The monitored moving average at time t is defined asM₁x² + x₁-12(sample size n=1.)Suppose the process mean shift between time t-1 and t is 1σ and t> 2. (i.e., the processmean of x, is shifted from µ at time t-1 to µ+σ at time t).(a) Write out the 2-sigma upper control limit for this MA chart.(b) Write out the distribution of Mr.(c) Calculate the detection power of the control charts designed in (a) at time t.(Remember the process is shifted at time t)

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Answered: A normally distributed quality…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose employers care about overall productivity Z, which is made up of two components, X and Y, such that Z=X+Y (and employers know this productivity function). Suppose there are two groups (male and female) whose average Zs are the same (i.e. Z_M =Z_F), but X_M < X_F and Y_M > Y_F (and again, employers know these population averages). (Averages are given by bold font.) Researchers decide to run a resume-based audit study where they randomize names based on gender (using typically male or female names) but hold constant Y. They provide no information on X. Which of the following results would provide suggestive evidence of statistical discrimination? A. The call-back rate is the same for both sexes. B. We can't use differences in call-back rates to find evidence of statistical discrimination.C. The call-back rate is higher for women than for men. D. The call-back rate is higher for men than for women.
1.Consider the following two simple regression models : Model I : Y, = B, + B,X, + µ; : Y, = a, +a, (X, - )+v, Model II (1) What is the estimator for B1? What is the estimator for a1? Are they the same to each other? Do they have the same variance? (2) What is the estimator for B2? What is the estimator for a2? Are they the same to each other? Do they have the same variance?
55. Consider the following partial computer output for a multiple regression model. Predictor Coefficient (b;) Standard Dev (Sb) Constant 99.3883 XI X2 X3 -0.007207 0.0031 0.0011336 0.00122 0.9324 0.373 The calculated value of the t statistic for X, is
The relationship between body mass index (BMI) and systolic blood pressure in males 50 years of age is investigated. A random sample of n = 13 males is selected and their BMI and systolic blood pressures are measured. Let X be the body mass index (BMI) and Y the systolic blood pressure of males, 50 years of age. Given: The average and variance of the BMI is X = 26 and Var(X) = 15.026. The average and variance of the systolic blood pressure is Y = 126 and Var(Y) = 423. The covariance between X and Y is Cov(X,Y) = 69.87. For the estimated regression equation Y = Bo + B, X, it was found that B1 = 4.65.
Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. The decrease in blood pressure y will vary about this subpopulation mean. What is the distribution of y for this subpopulation?
If x is a normally distributed variable with µ = 100 and σ = 5, find the lower and upper x values that will include 90% of the data. Lower x value = Upper x value =
Fifty male subjects drank a measured amount x (in ounces) of a medication and the concentration y (in percent) in their blood of the active ingredient was measured 30 minutes later. The sample data are summarized by the following information: n = 50 Ex = 112.5 Ex? = 356.25 %3D Ey = 4.83 Ey = 0.667 Exy = 15.255 0 < x < 4.5 Or= 0.875 Or= 0.709 Or= -0.846 Or=0.460 Or= 0.965
i)Fix the standard deviation of variance at sigma(0)=1.Sketch the graphs for N(-2,1) „N(0.1) ,N(2,1). ii)Fix the mean at =O.Then sketch the graphs for N(0,1) N(0,2), N(0,3).Interpret the graphs in terms of the distribution of the data about the mean.
The population mean will always be the same as the mean of all possible X¯ that can be computed from samples of size 21.
Consider house rent prediction problem where you are supposed to predict price of a house based on just its area. Suppose you have n samples with their respective areas, x(¹), x(²),...,x(n), their true house rents y(¹), y(²),..., y(n). Let's say, you train a linear regressor that predicts ƒ (x(i)) : = 0 + 0₁x¹). The parameters and ₁ are scalars and are learned by minimiz- ing mean-squared-error loss through gradient descent with a learning rate a. Answer the following questions. 1. Express the loss function(L) in terms of x(i),y(i), n, 00, 0₁. 2. Compute L მძი ƏL 3. Compute 20₁ 4. Write update rules for 0 and 0₁
Consider a simple linear regression model Yi = Bo + B1xi + Ei, i= 1,2, 3 with x; = i/3 for i = 1, 2, 3. Assume that %3| E1 1 -1 0 E = E2 ~ N -1 E3. 3 What is the smallest variance for an unbiased estimate of B1?
Consider the forecasting model with a simple, linear trend: It = ß1 + Bzt + et Where t is the index for t = 1, 2, ..., T. The OLS estimator of B1, B2 is: E (4t – Ht)(t – t) B2 = Bi = y – Bạf Where "bars" standards for the sample mean e.g. t = E-1 Yt. a Using those formulas, derive the OLS estimator of the regression yt = a1+a2(t – 1) + Et. Compare to Bị and B2. 81 + 82t + ɛt. b Again, using those formulas, derive the OLS estimator of the regression Yt/1000 Compare to B1 and B2.

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