Question

Costs are rising for all kinds of medical care. The mean monthly rent at assisted living facilities was reported to have increased 17% over the last five years to $3486. Assume this cost estimate is based on a sample of 120 facilities, it can be assumed that the population standard deviation is σ = $650.

Provide a 90% confidence interval for the population mean. (Round to two decimal places) __________and __________

Provide a 95% confidence interval for the population mean. (Round to two decimal places) __________and __________

Provide a 99% confidence interval for the population mean. (Round to two decimal places) __________and __________

Answer 1

90% Confidence interval:

For 90% CI, z = 1.645

So,

Margin of error = 1.645*650/ = 97.61

Hence,

90% confidence interval will be:

(3486 - 97.61) and (3486 + 97.61)

3388.39 and 3583.61

95% Confidence interval:

For 95% CI, z = 1.96

So,

Margin of error = 1.96*650/ = 116.30

Hence,

95% confidence interval will be:

(3486 - 116.30) and (3486 + 116.30)

3369.70 and 3602.30

99% Confidence interval:

For 99% CI, z = 2.576

So,

Margin of error = 2.576*650/ = 152.85

Hence,

95% confidence interval will be:

(3486 - 152.85) and (3486 + 152.85)

3333.15 and 3638.85