4. In a population of 10,000 businesses, we want to estimate the average sales Ỹ. 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), ^ - Y = 5.2 x 106 Euros (average sales in the sample), - X = 45 employees (sample mean), - s² = 25 x 10¹º (sample variance of yk), y = 15 (sample variance of x1), 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 Ỹ. 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), ^ - Y = 5.2 x 106 Euros (average sales in the sample), - X = 45 employees (sample mean), - s² = 25 x 10¹º (sample variance of yk), y = 15 (sample variance of x1), 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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Transcribed Image Text:4. In a population of 10,000 businesses, we want to estimate the average
sales Ỹ. 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),
^
- Y = 5.2 x 106 Euros (average sales in the sample),
- X = 45 employees (sample mean),
- s² = 25 x 10¹º (sample variance of yk),
y
= 15 (sample variance of x1),
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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