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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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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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