Question

A study was conducted to determine the average age of marriage. 15 people were asked how old they were when they got married. The average age was 30, and it may be assumed that the population standard deviation is 4. a) Calculate the 95% confidence interval for the age of marriage. b) How large does the sample size have to be, for the sample mean to be within 1 year of the population mean?

Answer 1

a)

sample mean 'x̄=	30.000
sample size    n=	15.00
std deviation σ=	4.000
std error ='σx=σ/√n=	1.0328

for 95 % CI value of z=		1.960
margin of error E=z*std error =		2.02
lower bound=sample mean-E=		27.9758
Upper bound=sample mean+E=		32.0242
from above 95% confidence interval for population mean =(27.98,32.02)

b)

here confidence interval is not given, assuming it to be 95%:

	for95% CI crtiical Z          =	1.960
	standard deviation σ=	4
	margin of error E =	1
required sample size n=(zσ/E)2                  =		62