Answered: Suppose you need to compute a 90%…

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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Question

Suppose you need to compute a 90% confidence interval for a population mean. a. If you assume the population variance is 10, what is the minimum sample size needed to create a confidence interval that is no larger than 1 unit wide (±1/2 units)? b. If you assume the population variance is 20, what is the minimum sample size needed to create a confidence interval that is no larger than 1 unit wide (±1/2 units)? c. If you assume the population variance is 20, what is the minimum sample size needed to create a confidence interval that is no larger 2 units wide (±1 unit)? Note that when the population variance is 20, the population standard deviation is 4.47. So the answer to d is also the answer to a case where the standard deviation is 4.47. d. Suppose the standard deviaiton is 8.94 (twice as large as 4.47). What is minimum sample size needed to create a 90% confidence interval that is 1 unit wide? e. Is the increase in the minimum sample size proportional to the 2x increase in the standard deviation (compare the answer to e to the answer to d)? Why or why not? f. Is an increase in the minimum sample size proportional to an increase in the variance (compare the answer to a to the answer to b)? Why or why not?

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