Question

A simple random sample of 60 items resulted in a sample mean of 89. The population standard deviation is 18.

a. Compute the 95% confidence interval for the population mean

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean

c. What is the effect of a larger sample size on the margin of error?

-increase - decrease -same - cannot determine

Answer 1

a)

sample mean 'x̄=	89.000
sample size    n=	60.00
std deviation σ=	18.000
std error ='σx=σ/√n=	2.3238

for 95 % CI value of z=		1.960
margin of error E=z*std error =	4.55
lower bound=sample mean-E=	84.4455
Upper bound=sample mean+E=	93.5545

from above 95% confidence interval for population mean =(84.45,93.55)

b)

sample size    n=	120.00
std deviation σ=	18.000
std error ='σx=σ/√n=	1.6432

for 95 % CI value of z=		1.960
margin of error E=z*std error =	3.22
lower bound=sample mean-E=	85.7795
Upper bound=sample mean+E=	92.2205

from above 95% confidence interval for population mean =(85.78,92.22)

c)

effect of a larger sample size on the margin of error : decrease