INTERVAL ESTIMATION

Question

Jakarta is a city that is densely populated. The average apartment rental cost has reached IDR 3,000,000 per month with a standard deviation of IDR 700,000 per month. If 50 tenants are taken, the average apartment rent will be IDR 2,500,000 per month. Determine the confidence interval for the amount of residential rent in Jakarta with a confidence level of 95% and whether the parameter for the average apartment rent in Jakarta is reasonable is IDR 3,000,000!

Answer 1

To find the confidence interval for the average residential rent in Jakarta given the data provided, we’ll use

the formula for the confidence interval of a sample mean:

CI = ¯x ± z

σ

√

n

Where: - ¯x = Sample mean (in this case, IDR 2,500,000) - σ = Population standard deviation (IDR 700,000)

- n = Sample size (50 tenants) - z = z-value for the given confidence level. For a 95% confidence level, the

z-value is approximately 1.96.

Plug in the numbers:

CI = 2, 500, 000 ± 1.96

700, 000

√50

CI = 2, 500, 000 ± 1.96(98, 994.949)

CI = 2, 500, 000 ± 194, 190.939

So, the 95% confidence interval for the average residential rent in Jakarta is:

(2, 305, 809.06, 2, 694, 190.94)

Next, we want to determine if the parameter for the average apartment rent in Jakarta being IDR 3,000,000

is reasonable.

To do this, we’ll see if IDR 3,000,000 lies within our 95% confidence interval. Since the range (2,305,809.06,

2,694,190.94) does not include IDR 3,000,000, we would conclude that, based on our sample of 50 tenants,

the parameter for the average apartment rent in Jakarta being IDR 3,000,000 does not seem reasonable at

the 95% confidence level.