Question

The birth weight in the United States has a standard deviation of σ = 575. A random sample of n = 30 birth weights give ¯x = 3189. (a) Find a 90% confidence interval and interpret it. [3] (b) Suppose now σ is unknown but a sample size of n = 15 is taken yielding a sample standard deviation of s = 538. Find the 90% confidence interval for µ again. (c) Suppose σ is unknown again but a sample size of n = 255 is taken yielding a sample standard deviation of s = 582. Find the 90% confidence interval for µ again

Answer 1

a)

sample mean 'x̄=	3189
sample size   n=	30
population std deviation σ=	575
std error 'σx=σ/√n=	104.9801569
for 90% CI, value of z=		1.644853627
margin of error E=z*std error    =		172.6769918
lower bound=sample mean-E =		3016.323008
Upper bound=sample mean+E =		3361.676992
from above 90% confidence interval for population mean =(3016.323,3361.6769)

we are 90% confidence that population mean is between in the above interval.

b)

sample mean 'x̄=	3189
sample size   n=	15
sample std deviation s=	538
std error 'sx=s/√n=	138.91
for 90% CI; and 14 df, value of t=		1.761310136
margin of error E=t*std error    =		244.665357
lower bound=sample mean-E =		2944.334643
Upper bound=sample mean+E =		3433.665357
from above 90% confidence interval for population mean =(2944.3346,3433.6653)

c)

sample mean 'x̄=	3189
sample size   n=	255
sample std deviation s=	582
std error 'sx=s/√n=	36.446
for 90% CI; and 254 df, value of t=		1.650874791
margin of error E=t*std error    =		60.16820154
lower bound=sample mean-E =		3128.831798
Upper bound=sample mean+E =		3249.168202
from above 90% confidence interval for population mean =(3128.8317,3249.1682)