3. Let X, X2, .. X5, be a random sample from apopulation having mean u and variance o?, and letô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be twoestimates of u.* Which of these two estimators is unbiased?* Which is the better estimator, and why?%3D

Answered: Image /qna-images/answer/f238d627-1489-4949-b6d9-6561acf7dc8d.jpg

Answered: 3. Let X, X2, .. X5, be a random sample…

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 computer while calculating correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results: ΣΧ = 125, ΣΧ2 = 650, ΣῪ = 100, n = 25, ΣΥ2 = 460, EXY = 508 If was, however, later discovered at the time of checking that he had copied down two pairs as X Y while the correct values were X Y Obtain the correct value of correlation 6 14 8 12 9 6 8 coefficient. 6
Consider a hypothesis test of difference of means for two independent populations x1 and x2.
A simple random sample without replacement was used to select 5 clusters from a population of 29 clusters. From each selected sample cluster simple random sampling without replacement was used to select samples of secondary units. For this data find an estimate of the population total and the population mean along with their estimated variances. clmemb clsize yval [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,] [21,] [22,] [23,] [24,] [25,] [26,] [27,] [28,] [29,] [30,] [31,] [32,] [33,] 1 20 46.07 20 45.54 20 43.07 1 1. 1 20 49.29 1 20 44.35 1 20 45.21 2 33 44.11 2 33 42.19 2 33 44.42 2 33 40.05 2 33 43.88 2 33 47.45 2 33 40.41 2 33 43.24 3 22 35.42 3 22 35.46 3 22 36.34 3 22 35.25 4 40 38.67 4 40 34.73 4 40 39.28 4 40 35.26 4 40 39.84 4 40 40.32 4 40 40.03 4 40 38.15 4 40 38.69 4 40 39.38 18 47.48 18 44.78 5 18 44.37 18 44.97 5 18 49.20
1. One difference between ANOVA and regression is: a) ANOVA is for statistical inference, whereas regression is not b) a regression line accounts for variability, whereas variability is not a concept in ANOVA c) in regression, we estimate a slope, whereas in ANOVA, we estimate mean differences d) ANOVA bases its inferences on samples, whereas regression bases its inferences on populations e) ANOVA and regression are not different at all, they are exactly the same f) ANOVA features p-values, whereas regression does not
Two computer companies are offering new software to universities. Let X and Y denote the number of software installed in three major universities by these two companies. Suppose that the variance of X is 539, the variance of Yis 754, and the covariance of X and Yis 183.50. a) Calculate the correlation coefficient (p) Select one: a. 0.287 b. 0.857 c. None of the answers d. 0.928
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…
A research study was conducted about gender differences in 'sexting'. The researcher believed that the proportion of girls involved in 'sexting' is different from the proportion of boys involved. The data collected in the spring of among a random sample of middle and high school students in a large school district in is summarized next: out of 380 females 43 sent 'sexts' and out of 410 males 64 sent 'sexts'. Is the proportion of girls sending sexts different from the proportion of boys 'sexting'? Choose the appropriate procedure. Procedure: Assumptions: (select everything that applies) Population standard deviations are known Normal populations Sample sizes are both greater than 30 Population standard deviation are unknown but assumed equal Paired samples Population standard deviation are unknown Simple random samples The number of positive and negative responses are both greater than 10 for both samples Independent samples
The aim of a study is to test the ratio of variances in the weight of two groups of rats being under a certain drugs A ( group 1) and B ( group 2). A random sample of 17 rats was selected from group 1and 11 rats from group 2, Then their weight were recorded. The results are shown in the following table 2 J غير مجاب عليه بعد الدرجة من 0 2.0 sd Median Mean n 3.0 3.5 17 group 1 2.0 2.20 11 group 2 علم هذا السؤال 1.05 1.15 F19,16,0.025 =0.386 F15,12,0.05 =0.404 F16,10,0.025=0.335 F19.16,0.05 =0.451 F15,12,0.1=0.496 F1610,0.05=0.401 F16,19,0.025 =0.371 F1215,0.05 =0.382 F10,16,0.025 =0.286 F16,19,0.05 =0.437 F1215,0.1=0.475 F10,16,0.05=0.354 Construct a 95% confidence interval for the ratio of the variances. [ Write only the final result in the box below ] 直 a
Assume a population with 5 elements: X1-0, X2-1, X3-2. X4-3,X5-4. Calculate mean and variance of X for random samples of size 3 taken with replacement Provide a numerical answer only.
Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected. Friday the 6th: Friday the 13th: 10 10 13 11 13 69 11
An "extraneous variable" is not a problem unless it with the independent variable O is identical systematically co-varies is not correlated Wait! An "extraneous variable" is by definition never a problem, that's what "extraneous" means.
3) Over repeated samples, the sample mean is considered a random variable. Is this statement TRUE or FALSE? Select one: True False 4) If the sample correlation coefficient has a value different from zero, this automatically means that the correlation in the population is also different from zero. Is this statement correct? Explain.

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3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be two estimates of u. ô, = 2x, X +X, +X,- X) %3D *Which of these two estimators is unbiased? Which is the better estimator, and why?