Question

A simple random sample of size n is drawn. The sample​ mean, x ​, is found to be 19.5​, and the sample standard​ deviation, s, is found to be 4.6.

a) Construct a 95% Confidence interval about μ if the sample size n, is 35

(Use ascending order to round to two decimal places as needed

lower bound= Upper bound=

b) Construct a 95% Confidence interval about μ if the sample size n, is 61

lower bound= Upper bound =

(a). How does increasing the level of confidence affect the size of the margin of​ error, E?

A.The margin of error increases.

B.The margin of error decreases.

C.The margin of error does not change

d) If the sample size is

Construct a 99% Confidence interval about μ if the sample size n, is 35

lower bound= Upper bound =

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. The margin of error increases.

B.The margin of error decreases.

C.The margin of error does not change.

3. If the sample size is 18 what conditions must be satisfied to compute the confidence​ interval?

A.The sample size must be large and the sample should not have any outliers.

B.The sample data must come from a population that is normally distributed with no outliers.

C.The sample must come from a population that is normally distributed and the sample size must be large.

Answer 1

Mean () = 19.5
Standard deviation (s) = 4.6
a) Sample size (n) = 35

Confidence interval(in %) = 95
z @ 95.0% = 1.96
Since we know that

Required confidence interval =
Required confidence interval = (19.5-1.524, 19.5+1.524)
Required confidence interval = (17.976, 21.024)

b) Sample size (n) = 61
Confidence interval(in %) = 95
z @ 95.0% = 1.96
Since we know that

Required confidence interval =
Required confidence interval = (19.5-1.1544, 19.5+1.1544)
Required confidence interval = (18.3456, 20.6544)

c) As level of confidence increases sizo of the margin of error. E increases because increasing confidence interval increases the z-value as well. margin of error is directly propotional to z-value

d) Sample size (n) = 35
Confidence interval(in %) = 99
z @ 99.0% = 2.576
Since we know that

Required confidence interval =
Required confidence interval = (19.5-2.0029, 19.5+2.0029)
Required confidence interval = (17.4971, 21.5029)