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Let X1,...,X, be a random sample from a normal distribution N(u, o2). (a) Find a 90% confidence interval for u based on the data for which X = 19.3 and n = 16 if it is known that o² = 9. (b) By using the information in (a), find a one-sided lower 90% confidence interval for u. Also, find a one-sided upper 90% confidence interval for u. (c) Suppose now that o? is unknown. Find a 90% confidence interval for u if X = 19.3, S? = 10.24, and n = (d) If o² = 9, what sample size is needed to achieve a 90% confidence interval for u 16.

Let X1,...,X, be a random sample from a normal distribution N(u, o2). (a) Find a 90% confidence interval for u based on the data for which X = 19.3 and n = 16 if it is known that o² = 9. (b) By using the information in (a), find a one-sided lower 90% confidence interval for u. Also, find a one-sided upper 90% confidence interval for u. (c) Suppose now that o? is unknown. Find a 90% confidence interval for u if X = 19.3, S? = 10.24, and n = (d) If o² = 9, what sample size is needed to achieve a 90% confidence interval for u 16.

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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Let X1,..., X, be a random sample from a normal distribution N(u, o²). (a) Find a 90% confidence interval for u based on the data for which X = 19.3 and n = 16 if it is known that o? = 9. (b) By using the information in (a), find a one-sided lower 90% confidence interval for u. Also, find a one-sided upper 90% confidence interval for u. (c) Suppose now that o is unknown. Find a 90% confidence interval for u if X = 19.3, S? = 10.24, and n = 16. (d) If o? = 9, what sample size is needed to achieve a 90% confidence interval for u of length 2?
Transcribed Image Text:Let X1,..., X, be a random sample from a normal distribution N(u, o²). (a) Find a 90% confidence interval for u based on the data for which X = 19.3 and n = 16 if it is known that o? = 9. (b) By using the information in (a), find a one-sided lower 90% confidence interval for u. Also, find a one-sided upper 90% confidence interval for u. (c) Suppose now that o is unknown. Find a 90% confidence interval for u if X = 19.3, S? = 10.24, and n = 16. (d) If o? = 9, what sample size is needed to achieve a 90% confidence interval for u of length 2?
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