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4. In a population of 10,000 businesses, we want to estimate the average sales Y For that, we sample n = = 100 businesses using simple random sampling. Furthermore, we have at our disposal the auxiliary information 'number of employees', denoted by x, for each business. The data coming from the sample are: - - X = 50 employees (true mean for x ), - Ŷ = 5.2 × 10 Euros (average sales in the sample), - X = 45 employees (sample mean), - s² = 25 x 1010 (sample variance of y₁), - 2 - s² = 15 (sample variance of x^), x p=0.80 (sample linear correlation coefficient between x and y ), a. Calculate the ratio estimate of Ỹ. Is this estimate unbiased or biased? Explain. b. What is the ‘true' variance formula for this estimate? c. Calculate an estimate of the true variance. Is the variance estimate unbiased or biased? Explain. d. Give a 95% confidence interval for Y.

4. In a population of 10,000 businesses, we want to estimate the average sales Y For that, we sample n = = 100 businesses using simple random sampling. Furthermore, we have at our disposal the auxiliary information 'number of employees', denoted by x, for each business. The data coming from the sample are: - - X = 50 employees (true mean for x ), - Ŷ = 5.2 × 10 Euros (average sales in the sample), - X = 45 employees (sample mean), - s² = 25 x 1010 (sample variance of y₁), - 2 - s² = 15 (sample variance of x^), x p=0.80 (sample linear correlation coefficient between x and y ), a. Calculate the ratio estimate of Ỹ. Is this estimate unbiased or biased? Explain. b. What is the ‘true' variance formula for this estimate? c. Calculate an estimate of the true variance. Is the variance estimate unbiased or biased? Explain. d. Give a 95% confidence interval for Y.

MATLAB: An Introduction with Applications
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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4. In a population of 10,000 businesses, we want to estimate the average sales Y For that, we sample n = = 100 businesses using simple random sampling. Furthermore, we have at our disposal the auxiliary information 'number of employees', denoted by x, for each business. The data coming from the sample are: - - X = 50 employees (true mean for x ), - Ŷ = 5.2 × 10 Euros (average sales in the sample), - X = 45 employees (sample mean), - s² = 25 x 1010 (sample variance of y₁), - 2 - s² = 15 (sample variance of x^), x p=0.80 (sample linear correlation coefficient between x and y ), a. Calculate the ratio estimate of Ỹ. Is this estimate unbiased or biased? Explain. b. What is the ‘true' variance formula for this estimate? c. Calculate an estimate of the true variance. Is the variance estimate unbiased or biased? Explain. d. Give a 95% confidence interval for Y.
Transcribed Image Text:4. In a population of 10,000 businesses, we want to estimate the average sales Y For that, we sample n = = 100 businesses using simple random sampling. Furthermore, we have at our disposal the auxiliary information 'number of employees', denoted by x, for each business. The data coming from the sample are: - - X = 50 employees (true mean for x ), - Ŷ = 5.2 × 10 Euros (average sales in the sample), - X = 45 employees (sample mean), - s² = 25 x 1010 (sample variance of y₁), - 2 - s² = 15 (sample variance of x^), x p=0.80 (sample linear correlation coefficient between x and y ), a. Calculate the ratio estimate of Ỹ. Is this estimate unbiased or biased? Explain. b. What is the ‘true' variance formula for this estimate? c. Calculate an estimate of the true variance. Is the variance estimate unbiased or biased? Explain. d. Give a 95% confidence interval for Y.
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