Questions: Estimating a Population Question 3, 9.2.17 A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 106, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ it the sample size, n, is 18. (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. (c) Construct a 90% confidence interval about μ if the sample size, n, is 18. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. Lower bound: 103.4; Upper bound: 108.6 How does increasing the sample size affect the margin of error, E? A. As the sample size increases, the margin of error increases. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error stays the same. (c) Construct a 90% confidence interval about μ if the sample size, n, is 18. Lower bound: 101.9; Upper bound: 110.1 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? A. As the level of confidence increases, the size of the interval increases. B. As the level of confidence increases, the size of the interval decreases. C. As the level of confidence increases, the size of the interval stays the same.

Transcript text: Estimating a Population Question 3, 9.2.17 A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, $\overline{\mathrm{x}}$, is found to be 106 , and the sample standard deviation, s , is found to be 10. (a) Construct an $80 \%$ confidence interval about $\mu$ it the sample size, n , is 18. (b) Construct an $80 \%$ confidence interval about $\mu$ if the sample size, n , is 26. (c) Construct a $90 \%$ confidence interval about $\mu$ if the sample size, n , is 18. (d) Could wo have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? (b) Construct an $80 \%$ confidence interval about $\mu$ if the sample size, n , is 26. Lower bound: 103.4 ; Upper bound: 108.6 How does increasing the sample size affect the margin of error, E? A. As the sample size increases, the margin of error increases. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error stays the same. (c) Construct a $90 \%$ confidence interval about $\mu$ if the sample size, n , is 18. Lower bound: 101.9 ; Upper bound: 110.1 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? A. As the level of confidence increases, the size of the interval increases. B. As the level of confidence increases, the size of the interval decreases. C. As the level of confidence increases, the size of the interval stays the same.