Question

Based on a random sample of one-bedroom apartments in Boston, the 95% confidence interval for the average monthly rent of all one-bedroom apartments in Boston is ($1700, $2000).

(a) Give the margin-of-error in the study.

(b) Is it possible that the average monthly rent of all one-bedroom apartments in Boston is $1600?

(c) If there were more apartments in the sample, would the 95% confidence interval be longer, shorter or remain the same?

(d) If the number of apartments in the sample were kept the same as before, would a 99% confidence interval be longer, shorter or remain the same?

Answer 1

Ans:

a)Margin of error=(2000-1700)/2=150

b)No,as the above confidence interval does not include 1600 within its limits.

c)If sample size is increased,standard error of mean decreases,so margin of error decreases,so 95% confidence interval becomes shorter.

d)Larger the confidence level,larger the margin of error,so longer the confidence interval.