Answer:
Explanation:
Given that 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
Sample size n =120
Population std dev =
![\sigma = 650](https://img.qammunity.org/2020/formulas/mathematics/college/x39synysyp2dwt9hztfrdvhyi90pds6wsr.png)
Since sigma is known we can use Z critical values for confidence interval
a) 90% confidence interval estimate of the population mean monthly rent
=Mean±1.645*std error
=
![3486+/- (650)/(√(120) ) *1.645\\\\=(3476.239, 3496.761)](https://img.qammunity.org/2020/formulas/mathematics/college/yy74oc42bq69joqg4t88dzjj2lvn2hygpm.png)
b) 95% confidence interval estimate of the population mean monthly rent.
==Mean±1.96*std error
=
![3486+/- (650)/(√(120) )*1.96\\=(3474.37, 3497.63)](https://img.qammunity.org/2020/formulas/mathematics/college/wxson6ghk1nhsegz44hrpktg01maabmp4o.png)
c) 99% confidence interval estimate of the population mean monthly rent.
=Mean±2.58*std error
=
![3486+/- (650)/(√(120) )*2.58\\=(3470.691, 3501.309)](https://img.qammunity.org/2020/formulas/mathematics/college/6rvxdzc4ghlo1ee9rzkwhpysrcbqy81scd.png)
d) Width increases as confidence level increases. This is reasonable because margin of error increases due to increase in critical value.