Confidence Interval Solutions
1. You want to rent an unfurnished one-bedroom apartment in Durham, NC
next year. The mean monthly rent for a random sample of 60 apartments
advertised on Craigโs List (a website that lists apartments for rent) is
$1000. Assume a population standard deviation of $200. Construct a 95%
confidence interval.
($1000 โ 1.96*$200/sqrt(60), $1000 + 1.96*$200/sqrt(60))
($949.39, $1050.61)
We are 95% confident that the interval ($949.39, $1050.61)
covers the true mean monthly rent of Durham apartments listed on
Craigโs List.
2. To what population of apartments can you appropriately infer from your
sample in #1?
We can most accurately infer to Durham apartments listed on Craigโs List.
We should not infer to all apartments in Durham because we do not know
if apartments on Craigโs List are representative of all apartments in
Durham.
3. How large a sample of one-bedroom apartments above would be needed to
estimate the population mean within plus or minus $50 with 90%
confidence?
The z multiplier for a 90% confidence interval is 1.645. We want
z*ฯ/sqrt(n) to equal $50.
$๐๐ = ๐ โ ๐
๐=๐. ๐๐๐ โ๐๐๐
๐=๐๐๐
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Solve for n. sqrt(n) = 329/50 = 6.58. Square both sides and you get an n
equal to 43.3. To calculate a margin of error +/- $50, you would need to
randomly sample 44 rental apartments on Craigโs List.
