Question

Apartment rental rates. You want to rent an unfurnished two-bedroom apartment in Dallas next year. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $1050. Assume that the monthly rents in Dallas follow a Normal distribution with a standard deviation of $220. Find a 95% confidence interval for the mean monthly rent for unfurnished two-bedroom apartments available in Dallas.

Answer 1

[$913.64, $1186.36]

Step-by-step explanation:

Data provided in the question:

Sample size, n = 10 apartments

Mean monthly rent = $1050

Standard deviation, s = $220

Confidence level = 95%

Now,

Confidence interval = Mean ±
`[z(s)/(\sqrt n)]`

here,

z = 1.96 for 95% confidence level from standard z table

thus,

Confidence interval = $1050 ±
`[1.96*\frac{\$220}{\sqrt {10}}]`

or

Confidence interval = $1050 ± 136.36

or

Confidence interval = [$1050 - $136.36, $1050 + $136.36]

or

Confidence interval = [$913.64, $1186.36]