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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2- Control charts for x ands with n = 4 are maintained on a quality characteristic. The parameters of these charts are as follows: 7 Chart UCL-201.88 Center line - 200.00 LCL-198.12 s Chart UCL-2.266 Center line - 1.000 LCL-0 Both charts exhibit control. Specifications on the quality characteristic are 197.50 and 202.50. What can be said about the ability of the process to produce product that conforms to specification?
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.
(d) For k satisfying -8 < k < k + 4 < 8, compute P(k < X < k + 4). (Round your answer to two decimal places.)
2. The 2 data sets are replicates of pH values of an alkaline solution (set A) and acidic solution (set B). (1) which is more precise? (2) which is more accurate? 11.2, 10.7, 10.9, 11.3, 11.5, 10.5, 10.8, 11.1, 11.2, 11.0 (x, = 10.7) B) 5.2, 6.0, 5.2, 5.9, 6.1, 5.5, 5.8, 5.7, 5-7, 6.o (x = 5.8) %3D
Composites are materials that are made by embedding a fiber, such as glass or carbon, inside a matrix, such as a metal or a ceramic. Composites are used in engineering structures, and their degradation when subjected to whether conditions is an important issue. In an experiment to investigate the effect of the moisture on a certain kind of composite, the weight gains of a collection of n=28 samples of composite subjected to water diffusion were obtained. The sample mean is x=0.42% with a sample std. of S=0.04% Can we 95% confident from the results of this experiment that the average weight gain for composites of this kind is smaller than 0.43%?
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.
Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.
A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
) You are considering the relationship between annual returns on the S&P 500 index (January 31 to January 31) and annual changes in the unemployment rate. You define:S = annual % change in the S&P500 (SPX)U = annual % change in the unemployment rateYou consider the following univariate relationship:Si = b0 + b1Ui + εiYou have data on annual changes in the unemployment rate and the S&P500 (SPX) from 2002 through 2020 (19 observations) and you want to use the data to estimate the regression coefficients (intercept b0 and slope b1)You are given the following statistics: Statistic Value Cov(U,S) -0.025043 Var(U) 0.034590 E(U) -0.001530 E(S) 0.064267 TSS 0.627907 RSS 0.326368 Compute the estimated coefficients for the intercept (b0) and slope (b1) and the R2 So far in 2021, the unemployment rate has decreased by 24% (from 6.3 percent to 4.8 percent). If the unemployment rate holds steady until the end of the year, resulting in an…
Lecture(8.8): The amount of time people engage in physical activity mat be related to health outcome. Those who report that they spend more than 15 hours are put into one while those who spend less 10 were put into another group. (Those who fall in between 10 and 15 were left out of the study); The reaearcher then ask the participants to wear a monitor for one month. The average time in minutes is recorded and shown below . Is there any evidence that on average people who watch less than 10 hours watching televsion spend more time on physical activity.?. Test the hypotheses at (alpha=0.05) using the 5 step procedure <10 hours 75 63 118 35 82 >15 hours 62 6 78 43 22 33
5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?
Urinary fluoride concentration (in parts per million) was measured for both a sample of livestock that had been grazing in an area previously exposed to fluoride pollution and a similar sample of livestock that had grazed in an unpolluted region. Do the accompanying data indicate strongly that the mean fluoride concentration for livestock grazing in the polluted region is larger than that for livestock grazing in the unpolluted region? Assume that the distributions of urinary fluoride concentration for both grazing areas have the same shape and spread. Use a significance level of 0.05. Group 1 (Polluted): 21.3 || 18.7 || 23.0 || 17.1 || 16.8 || 20.9 || 19.7 Group 2 (Unpolluted): 14.2 || 18.3 || 17.2 || 18.4 || 20.0 What is/are the Mann-Whitney Rank Sum critical value(s) for this problem? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 43 b 56 n 58,33 d 60

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