A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, $\bar{x}$, is found to be 108, and the sample standard deviation, $s$, is found to be 10.
(a) Construct an 80% confidence interval about $\mu$ if the sample size, $n$, is 19.
(b) Construct an 80% confidence interval about $\mu$ if the sample size, $n$, is 27.
(c) Construct a 99% confidence interval about $\mu$ if the sample size, $n$, is 19.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
(a) Construct an 80% confidence interval about $\mu$ if the sample size, $n$, is 19.
Lower bound: ; Upper bound:
(Use ascending order. Round to one decimal place as needed.)
(b) Construct an 80% confidence interval about $\mu$ if the sample size, $n$, is 27.
Lower bound: ; Upper bound:
(Use ascending order. Round to one decimal place as needed.)
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 99% confidence interval about $\mu$ if the sample size, $n$, is 19.
Lower bound: ; Upper bound:
(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?
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 increases.
