Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbarx​, is found to be 115115​, and the sample standard​ deviation, s, is found to be 1010. ​(a) Construct aa 9898​% confidence interval about muμ if the sample​ size, n, is 1111. ​Lower bound _____; Upper bound

(b) Construct aa 9898​% confidence interval about muμ if the sample​ size, n, is 1717. ​ Lower bound _____; upper bound ______

(c) Construct aa 9999​% confidence interval about muμ if the sample​ size, n, is 1111. Lower bound _____; upper bound _______

Answer 1

a)

b)

sample mean 'x̄=	115
sample size   n=	17
sample std deviation s=	10
std error 'sx=s/√n=	2.4254
for 98% CI; and 16 df, value of t=		2.583487185
margin of error E=t*std error    =		6.265876793
lower bound=sample mean-E =		108.7341232
Upper bound=sample mean+E =		121.2658768
from above 98% confidence interval for population mean =(108.7341,121.2658)

c)

sample mean 'x̄=	115
sample size   n=	11
sample std deviation s=	10
std error 'sx=s/√n=	3.0151
for 99% CI; and 10 df, value of t=		3.169272673
margin of error E=t*std error    =		9.555716649
lower bound=sample mean-E =		105.4442834
Upper bound=sample mean+E =		124.5557166
from above 99% confidence interval for population mean =(105.4443,124.5557)