Let X₁,..., Xn each be independently distributed N(μ, o2) where o = 3.0. Suppose the sample mean is x = Xi = = 58.3 File Preview n Zi=1 (a) Compute a 95% and a 99% CI for u when n = 25. (b) Compute a 95% and a 99% CI for u when n = 10. Now assume that o is unknown and gets estimated by the sample SD s = 4.3. (c) Compute a 95% and a 99% CI for u when n = 25. (d) Compute a 95% and a 99% CI for u when n = 10. Compare your answers for fixed n, and fixed confidence level, respectively. In addition, would the confi- dence interval get larger or smaller if o is unknown for fixed sample size and confidence level? Explain why.
Let X₁,..., Xn each be independently distributed N(μ, o2) where o = 3.0. Suppose the sample mean is x = Xi = = 58.3 File Preview n Zi=1 (a) Compute a 95% and a 99% CI for u when n = 25. (b) Compute a 95% and a 99% CI for u when n = 10. Now assume that o is unknown and gets estimated by the sample SD s = 4.3. (c) Compute a 95% and a 99% CI for u when n = 25. (d) Compute a 95% and a 99% CI for u when n = 10. Compare your answers for fixed n, and fixed confidence level, respectively. In addition, would the confi- dence interval get larger or smaller if o is unknown for fixed sample size and confidence level? Explain why.
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 \( X_1, \ldots, X_n \) each be independently distributed \( N(\mu, \sigma^2) \) where \( \sigma = 3.0 \). Suppose the sample mean is
\[
\bar{x} = \frac{1}{n} \sum_{i=1}^{n} X_i = 58.3
\]
(a) Compute a 95% and a 99% CI for \( \mu \) when \( n = 25 \).
(b) Compute a 95% and a 99% CI for \( \mu \) when \( n = 10 \).
Now assume that \( \sigma \) is unknown and gets estimated by the sample SD \( s = 4.3 \).
(c) Compute a 95% and a 99% CI for \( \mu \) when \( n = 25 \).
(d) Compute a 95% and a 99% CI for \( \mu \) when \( n = 10 \).
Compare your answers for fixed \( n \), and fixed confidence level, respectively. In addition, would the confidence interval get larger or smaller if \( \sigma \) is unknown for fixed sample size and confidence level? Explain why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1aaff698-d6d9-432c-a8ab-5a03f6066bc1%2F767e0c09-67e2-402f-836a-f08c7d10b093%2Ffcnyulj_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( X_1, \ldots, X_n \) each be independently distributed \( N(\mu, \sigma^2) \) where \( \sigma = 3.0 \). Suppose the sample mean is
\[
\bar{x} = \frac{1}{n} \sum_{i=1}^{n} X_i = 58.3
\]
(a) Compute a 95% and a 99% CI for \( \mu \) when \( n = 25 \).
(b) Compute a 95% and a 99% CI for \( \mu \) when \( n = 10 \).
Now assume that \( \sigma \) is unknown and gets estimated by the sample SD \( s = 4.3 \).
(c) Compute a 95% and a 99% CI for \( \mu \) when \( n = 25 \).
(d) Compute a 95% and a 99% CI for \( \mu \) when \( n = 10 \).
Compare your answers for fixed \( n \), and fixed confidence level, respectively. In addition, would the confidence interval get larger or smaller if \( \sigma \) is unknown for fixed sample size and confidence level? Explain why.
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