**Question 22**We denote the population variance with the symbol:- ○ \(\bar{x}\)- ○ \(\sigma\)- ○ \(N\)- ○ \(M\)- ○ \(\tilde{x}\)- ○ \(\mu\)- ○ \(s^2\)- ○ \(\sigma^2\)- ○ \(s\)- ○ \(n\)*Note: The correct choice for the population variance symbol is \(\sigma^2\).*

Answered: 22 We denote the population variance…

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-d
Prove that the sample variance is an unbiased estimator for the population variance. That is, show that
Complete the following table that lists all possible samples of n = 2 scores from the population. Use the first three rows (Samples a-c) as examples. Sample a b с d e f 9 h i Score 1 Score 2 1 Mean of 1 1 SS n-1 4 4 4 7 7 7 Mean of M column= column= 1 SS Mean of column = n 4 7 1 4 7 1 4 7 M = This EX n 1.00 2.50 This 4.00 2.50 4.00 5.50 4.00 5.50 7.00 This SS 0.00 Calculate the mean for all values in the M column, SS column and in column. Which values match the parameters of the population? Identify those statistics that were biased. Identify those statistics that were unbiased. n-1 4.50 18.00 SS n-1 0.00 4.50 18.00 SS 0.00 2.25 9.00 the mean u of the population. The sample mean is ▼ the variance o² of the population. Sis the variance 02 of the population. SS is n-1 estimate of u. estimate of 02. estimate of g².
nd markers without ink. Assume that the box contains 17 markers: 12 that contain ink and 5 tha ontain ink. A sample of 8 markers is selected and a random variable Y is defined as the number arkers selected which do not have ink. ow many different values are possible for the random variable Y? Part 2
27
NN II טה If X and Y are random variables with variances σ = 3 and 0² = 9, X and Y are not independent, and oxy = 1, then find the variance of the random variable Z = -9X+8Y-7.
Which of the following statements below is incorrect about Type II error? The larger the effect size, the smaller the power of the test will be. For a given probability of type I error, the probability of type II error can be reduced by increasing the sample size. The power of a test is equal to 1-3, where represents the probability that a hypothesis test does not reject a false null hypothesis. The effect size measures the distance between the true population proportion and the value assumed for it in the null hypothesis.
3. Can SAT scores predict college performance? Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation. A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58 The scatter diagram for the SAT score and GPA is given below: (a) Find the sample correlation coefficient r. Truncate to two decimal places. What does the value tell you about the data? (b) Find the equation of the least squares line . Truncate to four decimal places. What does the slope mean? (c) Find the value of the coefficient of determination . Truncate to two decimal places. What does this number mean? (d) What is the predicted GPA if a computer science major got a…
Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable x is the number of Mexican-Americans on the jury. x 0 1 2 3 4 5 6 7 8 9 10 11 12 P(x) 0.0000.000 0.0030 0.0160 0.0540 0.1210 0.1930 0.2260 0.1930 0.1210 0.0540 0.0160 0.0030 0.0000 A. Find the probability of exactly 2 Mexican-Americans among 12 jurors. P(2)equals= b. Find the probability of 2 or fewer Mexican-Americans among 12 jurors. c. Does 2 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? Why or why not?
Complete both tables on the remaining pages and show your work for at least three Equal Variances F Tests and at least five T tests. You must show at least one computation using Welch’s T Test and at least one computation using the 2-Sample T Test for Equal Means.(I don't know how to find the distribution or probability for the first chart)

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22 We denote the population variance with the symbol N M x σ 8² 0² $ O n