A simple random sample of size n is drawn from a population that is normally dis
ID: 3226085 • Letter: A
Question
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean is found to be 115, and the sample standard deviation, s, is found to be 10. (Round to 1 decimal place as needed)
(a) Construct anan 80% confidence interval about mu if the sample size, n, is 12.
(b) Construct anan 80% confidence interval about mu if the sample size, n, is 22.
(c) Construct aa 95% confidence interval about if the sample size, n, is 12.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Explanation / Answer
a) std error of mean =std deviation/(n)1/2 =2.887
for 80% CI and 11 degree of freedom ; t=1.3634
hence confiodence interval=sample mean -/+t*Std error =111.1 ; 118.9
b)
std error of mean =std deviation/(n)1/2 =2.132
for 80% CI and 21 degree of freedom ; t=1.323
hence confiodence interval=sample mean -/+t*Std error =112.2 ; 117.8
c)
std error of mean =std deviation/(n)1/2 =2.887
for 95% CI and 11 degree of freedom ; t=2.201
hence confiodence interval=sample mean -/+t*Std error =108.7 ; 121.3
d) No ; for non normallity the sample size should be at least equal to 30
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