Question

1. You want to rent an unfurnished one-bedroom apartment for next semester. You take a random sample of 10 apartments advertised in the local newspaper and record the monthly rent. Here are the sample data:

500, 650, 600, 505, 450, 550, 515, 495, 650, 395

1. Find the sample mean
2. Find the sample median
3. Find the standard deviation
4. Find the variance
5. Find the range
6. Construct a 95% confidence interval estimate of the population mean. (You may assume that the original population is normally distributed.)
7. Use a 0.05 significance level to test the claim that the mean rent of all advertised apartments is greater than $500 per month. Include all the important steps of your hypothesis test process.

Answer 1

a. 531

b. 510

c. 82.79

d. 6854.44

e. 255

f.

M = 531
Z = 1.96
s_M = √(82.79²/10) = 26.18

μ = M ± Z(s_M)
μ = 531 ± 1.96*26.18
μ = 531 ± 51.31

95% CI [479.69, 582.31]

g.