Theorem 3: Let x - (x1,X2 -- . Xp . .., x,) be a data set with a sample mean ĩ and asample variance S. Also, let y = (y. Y2 ..yp m, Ya) be a data set with a samplemean ỹ and a sample variance S. Finally, let z = x - y such thatz- (X1- yı, X2 – y2 -- .X - Ya... . , Xn – Yn).Show that i -i - ỹ.

x1,x2,...,xn is a data set with sample mean x and sample variance Sx2. And, y1,y2,....,yn is…

Answered: Theorem 3: Let x - (x1, X2 - m-, Xyo.…

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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Assume that the height of male students in a large university is normally distributed with mean 172.7 cm and variance 57.76 cm². (a) Suppose 80 random samples, each with 25 male students are obtained. In how many samples would you expect the sample mean to be between 169.66 cm and 173.46 cm? Give you answer to one decimal place. Answer: number of samples = (b) Suppose 6 random samples, each with 25 male students are obtained. Compute the probability that exactly 4 of the 6 samples will have its sample mean between 169.66 cm and 173.46 cm. Give your answer to two decimal places. Answer: probability=
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
Say you have two sets of data X1, ..., X10 and Y1,..., Y40. All of this data is considered independent. The first set of data are Normally distributed with mean B and variance 10. The second set of data are Normally distributed with mean y and variance 10. We are trying to estimate 0 = X = X; 18 + y. Consider the estimate ô = }X + Ÿ where 3 4 iX + Y where 10 vi=1 1 10 and Y = E Y;? 40 vi=1 40 (a) What is the mean, variance and distribution of 0? (b) What is the probability that 0 is larger than 1 away from 0? (c) What is the bias, variance and MSE of the estimate 0 for estimating 0?
Number 16
The frequency distribution table below is the net weight of a sample of candied fruit products in the food industry cans "ABC": - How many cans have a net weight of less than 20.2 grams. - If we want to compare about the distribution of net weight with the food company "XYZ" for the same type of product. And it is known that the average and variance is 20 grams and 0.04 grams. Which food company has an even distribution of net weight.
Suppose that we have disjoint normal populations A and B with equal but unknown population variances. Suppose we plan a sample of size 12 from from population A and a sample of size 6 from population B which we will pool to form the pooled variance. If the sample variance for the sample from population A is 25 and the sample variance for the sample from population B is 36, then what is the pooled sample variance?
/Skip/1 A beverage company has two bottling plants in different parts of the world. To insure uniformity in their product, the variances of the weights of the bottles at the two plants should be equal. But Stephanie, the company's vice president of quality assurance, suspects that the variance at bottling plant A is more than the variance at bottling plant B. To test her suspicions, Stephanie samples 37 bottles from bottling plant A and 33 bottles from bottling plant B, with the following results (in ounces): Bottling Plant A: 12.4, 12.4, 13.4, 14.3, 12.7, 12.7, 13.7, 12.4, 12.8, 12.4, 12.9, 12.7, 12.8, 13.3, 13.8, 12.7, 12.4, 11.9, 12.9, 13, 13.1, 12.4, 12.7, 12.6, 12.5, 13.3, 12.2, 13.3, 12.8, 12.7, 13.2, 13.1, 11.7, 13, 12.3, 13.1, 12.4 Bottling Plant B: 12.9, 12, 13.4, 12.4, 12.4, 12.9, 12.7, 12.1, 11.4, 13.1, 14.1, 12.5, 12.7, 11.5, 12.3, 12.7, 13.7, 12.6, 13.9, 12.7, 12, 12.5, 11.7, 13.6, 11.4, 13.6, 14, 12, 11.5, 12, 11.7, 13, 11.8 Perform a hypothesis test using a 3% level of…

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