Last year the Chronicle reported that average rent for a one

Last year the Chronicle reported that average rent for a one-bedroom apartment in Center City was $1229. Lucas just moved to town. He looked at 17 one-bedroom apartments and their average rent was $1350 with a standard deviation of $175. Treat Lucas’ apartment search as a simple random sample, assume that rents are normally distributed and test if rent for a one-bedroom apartment has gone up since last year at the =0.05 level of significance.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=1229
Alternate Hypothesis H1: U!=1229
Test Statistic
Population Mean(U)=1229
Given That X(Mean)=1350
Standard Deviation(S.D)=175
Number (n)=17
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=1350-1229/(175/Sqrt(17)
Zo =2.8508
| Zo | =2.8508
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.8508 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 2.8508 ) = 0.0044
Hence Value of P0.05 > 0.0044, Here we Reject Ho