Question

A group of statistics students decided to conduct a survey at Loyola Marymount University to find the mean number of hours students spent studying per week. a. They sampled 576 students and found the mean to be 20 hours. Assuming we know the population standard deviation is 7 hours, what is the confidence interval at the 95% level of confidence? b. They sampled 576 students and found the mean to be 20 hours. Assuming we know the population standard deviation is 7 hours, what is the confidence interval at the 99% level of confidence? What do you notice as the difference between the solution for (a) and (b)? c. They sampled 100 students and found the mean to be 21 hours. Assuming we don’t know the population standard deviation, but we estimate the sample standard deviation to be 6 hours, what is the confidence interval at the 95% level of confidence? d. Assuming we know the population standard deviation is 7 hours, what is the required sample size if the error should be less than 15 minutes with a 95% level of confidence?

Answer 1

a)

sample mean 'x̄=	20.000
sample size    n=	576.00
std deviation σ=	7.00
std error ='σx=σ/√n=	0.2917

for 95 % CI value of z=		1.96
margin of error E=z*std error =		0.572
lower bound=sample mean-E=		19.428
Upper bound=sample mean+E=		20.572
from above 95% confidence interval for population mean =(19.43,20.57)

b)

for 99 % CI value of z=		2.58
margin of error E=z*std error =		0.751
lower bound=sample mean-E=		19.249
Upper bound=sample mean+E=		20.751
from above 99% confidence interval for population mean =(19.25,20.75)

c)

sample mean 'x̄=	21.000
sample size   n=	100.00
sample std deviation s=	6.00
std error 'sx=s/√n=	0.6000

for 95% CI; and 99 df, value of t=		1.984
margin of error E=t*std error    =		1.190
lower bound=sample mean-E =		19.810
Upper bound=sample mean+E =		22.190
from above 95% confidence interval for population mean =(19.81,22.19)

d)

	for95% CI crtiical Z          =	1.960
	standard deviation σ=	7
	margin of error E =	0.25
required sample size n=(zσ/E)2                  =		3012