Question

A study based on a random sample of 17 reported a sample mean of 65 with a sample standard deviation of 4.

1. Calculate a 95% Confidence interval.

2. What is the margin of error?

3. If we calculated a 90% confidence interval, as compared to your answer in part b, would your margin of error increase: (choose one)

1. increase
2. decrease
3. stay the same

4. If we increase the sample size to 50 persons, but the reported sample mean and sample standard deviation stayed the same as in part a, would the 95% confidence interval get: (choose one)

1. wider
2. narrower
3. stay the same

Answer 1

1)

sample mean 'x̄=	65.000
sample size   n=	17.00
sample std deviation s=	4.000
std error 'sx=s/√n=	0.9701

for 95% CI; and 16 df, value of t=	2.120
margin of error E=t*std error    =	2.057
lower bound=sample mean-E =	62.9434
Upper bound=sample mean+E =	67.0566
from above 95% confidence interval for population mean =(62.94,67.06)

2)

margin of error =2.057 ~ 2.06

3)margin of error

decrease

4)

95% confidence interval get narrower