Question

You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a simple random sample of 30 apartments advertised in the local newspaper is $1,450. The standard deviation of the population is $220. Find a 99% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.

Answer 1

Answer: 99% confidence interval would be $(1346.37,1553.63)$

Step-by-step explanation:

Since we have given that

Sample size = 30

Sample mean = $1450

Standard deviation = $220

We need to find the 99% confidence interval.

So, z = 2.58

So, confidence interval would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1450\pm 2.58\times \dfrac{220}{\sqrt{30}}\\\\=1450\pm 103.63\\\\=(1450-103.63,1450+103.63)\\\\=(1346.37,1553.63)$

Hence, 99% confidence interval would be $(1346.37,1553.63)$