Question

you are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. interpret the results and compare the widths of the confidence intervals. if convenient, use technology to construct the confidence intervals.

a random sample of 55 home theater systems has a mean price of $113.00. Assume the population standard deviation is $16.50

Answer 1

1)for 90% CI:

sample mean 'x̄=	113.000
sample size    n=	55.00
std deviation σ=	16.500
std error ='σx=σ/√n=	2.2249

for 90 % CI value of z=		1.645
margin of error E=z*std error =		3.660
lower bound=sample mean-E=		109.34
Upper bound=sample mean+E=		116.66
from above 90% confidence interval for population mean =(109.34,116.66)

above interval gives 90% confidence to contain true value of population mean

for 95% CI:

for 95 % CI value of z=		1.960
margin of error E=z*std error =		4.361
lower bound=sample mean-E=		108.64
Upper bound=sample mean+E=		117.36
95% confidence interval for population mean =(108.64,117.36)
above interval gives 95% confidence to contain true value of population mean

95% confidence interval has larger width.