Question

2.

The average monthly rent for a one-bedroom home in San Francisco is $1229. A random

sample of 15 one-bedroom homes outside the city had a mean rent of $1350. At a = 0.05,

can we conclude that the rent outside the city differs from the rent in the city?

Answer 1

Answer

given,

average rent of one bed room = $1229

sample size = n = 15

Sample mean rent = $1350

Assuming standard deviation equal to $250

the test hypothesis is

H o: µ=1229

H a: µ not equal to 1229

now we know,

$t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t = \dfrac{\ 1350-\ 1229}{\dfrac{250}{\sqrt{15}}}$

     t = 1.875

from t- table

a=0.05, the critical value is  |t(0.025, d f= n-1 = 14)|=2.14

since t= 1.875 which is less than 2.14 we do not reject H o.

So we can not conclude that the monthly rent outside San Francisco differs from that in the city