A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 105, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about u if the sample size, n, is 16. (b) Construct a 98% confidence interval about μ if the sample size, n, is 26. (c) Construct a 99% confidence interval about μ if the sample size, n, is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 98% confidence interval about u if the sample size, n, is 16. Lower bound: 98.5; Upper bound: 111.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about if the sample size, n, is 26. Lower bound: 100.1; Upper bound: 109.9 (Use ascending order. Round to one decimal place as needed.) How does increasing the sample size affect the margin of error, E? O A. As the sample size increases, the margin of error stays the same. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error increases. (c) Construct a 99% confidence interval about μ if the sample size, n, is 16. Lower bound: 97.5; Upper bound: 112.5 (Use ascending order. Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. As the level of confidence increases, the size of the interval stays the same. B. As the level of confidence increases, the size of the interval decreases. OC. As the level of confidence increases, the size of the interval increases.
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 105, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about u if the sample size, n, is 16. (b) Construct a 98% confidence interval about μ if the sample size, n, is 26. (c) Construct a 99% confidence interval about μ if the sample size, n, is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 98% confidence interval about u if the sample size, n, is 16. Lower bound: 98.5; Upper bound: 111.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about if the sample size, n, is 26. Lower bound: 100.1; Upper bound: 109.9 (Use ascending order. Round to one decimal place as needed.) How does increasing the sample size affect the margin of error, E? O A. As the sample size increases, the margin of error stays the same. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error increases. (c) Construct a 99% confidence interval about μ if the sample size, n, is 16. Lower bound: 97.5; Upper bound: 112.5 (Use ascending order. Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. As the level of confidence increases, the size of the interval stays the same. B. As the level of confidence increases, the size of the interval decreases. OC. As the level of confidence increases, the size of the interval increases.
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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Transcribed Image Text:A simple random sample of size n is drawn from a population that is normally distributed. The
sample mean, x, is found to be 105, and the sample standard deviation, s, is found to be 10.
(a) Construct a 98% confidence interval about if the sample size, n, is 16.
(b) Construct a 98% confidence interval about μ if the sample size, n, is 26.
(c) Construct a 99% confidence interval about u if the sample size, n, is 16.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been
normally distributed?
Click the icon to view the table of areas under the t-distribution.
(a) Construct a 98% confidence interval about if the sample size, n, is 16.
Lower bound: 98.5; Upper bound: 111.5
(Use ascending order. Round to one decimal place as needed.)
(b) Construct a 98% confidence interval about μ if the sample size, n, is 26.
Lower bound: 100.1 ; Upper bound: 109.9
(Use ascending order. Round to one decimal place as needed.)
How does increasing the sample size affect the margin of error, E?
O A. As the sample size increases, the margin of error stays the same.
B. As the sample size increases, the margin of error decreases.
C. As the sample size increases, the margin of error increases.
(c) Construct a 99% confidence interval about μ if the sample size, n, is 16.
Lower bound: 97.5; Upper bound: 112.5
(Use ascending order. Round to one decimal place as needed.)
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the
size of the margin of error, E?
O A. As the level of confidence increases, the size of the interval stays the same.
OB. As the level of confidence increases, the size of the interval decreases.
OC. As the level of confidence increases, the size of the interval increases.
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