a) Let X,, X2..„X, are independent random samples taken from population with mean andvariance of u and o? respectively. Determine whether A is an unbiased estimator of uif,i= (X, +X, +.+Xr,)2b) A lecturer is investigating the proportion of students who are ready for online learning inSTA150 class. It is found that from previous study, 65% of the students are ready foronline learning. How large a sample is needed if the lecturer wishes to be 99%confidence with the margin of error is within 5%?c) A medical researcher has conducted a study that involved 200 hypertension patientsand 180 hypotension patients. It was found that 80 of those with hypertension and 108of those with hypotensionfor the difference between the two proportions of patients. Interpret the interval obtained.dizziness problems. Construct a 99% confidence interva

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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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A sample of n observations has a sample mean of �̅x= 100 and variance of σ2 =100. If a new observation is added, x below(n+1) = 100, the sample variance willa. Increaseb. Decreasec. Stay the same
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Q2 Suppose x1, x2, ... , xn have a sample mean ī and a sample variance s 1. Let y; = x; + 10, show that the sample mean and sample variance of Yi's are ¤ + 10 and s respectively. 2. Let y; = 2 × x;, show that the sample mean and sample variance of y;'s are 2 × ī and 4 × s respectively.
What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? |Ho: µ is ? |H: µ is ? In the context of this test, what is a Type II error? V? v when, in A Type II error is ? fact, u is ? | the hypothesis that u is ? Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? ?
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Let wages denote hourly wages, educ years of education, and exper years of experience, and suppose log(wages) = f1 + 62educ + B3exper +e where E[eleduc, exper] = 0. Let b1, b2, and bz be our estimates for B1, B2, and ß3 and r23 denote the sample correlation between {educ,}", and {exper, }". Which of the following statements is true? II O a. The variance of b3 does not depend on r23. O b. The variance of b, is increasing in E" (educ, – educ,)² (all else equal). O c. The variance of b2 is at least as large as o²/ E", (educ, - educ,)2 for o? Var(eleduc, exper). O d. The variance of b2 depends on the sign of r23. O e. The variance of b2 always increases as r23 increases (all else equal).
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Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?
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Let X1. X2.Xp are independent random samples taken from population with mean and variance of u and o? respectively. Determine whether A is an unbiased estimator of u if; à- n(X, +X; +..+x,)