Question

you want to rent an unfinished one bedroom apartment in west orange next year. the mean monthly rent for a simple random sample of 25 appartment advertised in the local newspaper is $1,6000 and the standard deviation is $240

find a 99% confidence interval for the mean monthly rent for unfurnished one bedroom apartment available for rent in this community

Answer 1

Here we need to find 99% confidence interval for the monthly rent for unfurnished one bedroom apartment

Xbar=16000

sd=240

n=25

We need to find z value for 0.5% area towards left and right side of the normal distribution

Z= (Xbar-mu)/(sd/sqrt(n))

mu=Xbar-Z*sd/sqrt(n)

Now the Z value for 0.5% area towards left and right side of the curve is -2.58 and +2.58 from Z table

mu=16000-2.58*240/sqrt(25)

mu=15876.16

&

mu=16000+2.58*240/sqrt(25)

mu=16123.84

Hence here we say that a 99% confidence interval for the mean monthly rent for unfurnished one bedroom apartment available for rent in this community is ranging from 15876.16 to 16123.84

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