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witcol386
09.12.2019 •
Mathematics
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 (the wall street journal, october 27, 2012). assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is σ = $650 . a) develop a 90% confidence interval estimate of the population mean monthly rent.
b) develop a 95% confidence interval estimate of the population mean monthly rent.
c) develop a 99% confidence interval estimate of the population mean monthly rent.
d) what happens to the width of the confidence interval as the confidence level is increased? does this seem reasonable? explain.
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Ответ:
Step-by-step 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](/tpl/images/0410/4801/762d9.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+/- \frac{650}{\sqrt{120} } *1.645\\\\=(3476.239, 3496.761)](/tpl/images/0410/4801/b6946.png)
b) 95% confidence interval estimate of the population mean monthly rent.
==Mean±1.96*std error
=![3486+/- \frac{650}{\sqrt{120} }*1.96\\=(3474.37, 3497.63)](/tpl/images/0410/4801/01d49.png)
c) 99% confidence interval estimate of the population mean monthly rent.
=Mean±2.58*std error
=![3486+/- \frac{650}{\sqrt{120} }*2.58\\=(3470.691, 3501.309)](/tpl/images/0410/4801/cba7d.png)
d) Width increases as confidence level increases. This is reasonable because margin of error increases due to increase in critical value.
Ответ:
Part A
Chorus:
Expontential growth = b*a^x
b = 15
a = 1.12 (a= r+1), r = 12%
Which gives a function of f(x) = 15*1.12^x
Band
Linear growth = ax+b
a = 2
b = 30
Which gives a function of g(x)=2x+30
Part B:
f(9) = 15*1.12^9 = 41.59
g(9) = 2*9+30 = 48
Part C:
This is probably problem solving, where you're allowed to use calculators and other softwares.
Therefore you can use different softwares, and make f(x) = g(x).
I did this, and got it to 10.95427141
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Ambitious