Commercial real estate prices and rental rates suffered substantial declines in
ID: 3175091 • Letter: C
Question
Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009 (Newsweek, July 27, 2009). These declines were particularly severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined by 40% or more. Even with such large declines, annual lease rates in Asia were still higher than those in many cities in Europe. Annual lease rates for a sample of 30 commercial properties in Hong Kong showed a mean of $1,114 per square meter with a standard deviation of $230. Annual lease rates for a sample of 40 commercial properties in Paris showed a mean lease rate of $989 per square meter with a standard deviation of $195.Assume that the population variances are equal.
A. On the basis of the sample results, can we conclude that the mean annual lease rate is higher in Hong Kong than in Paris? Conduct an appropriate hypothesis test. Use = .01.
Hypotheses (symbols and words):
Decision rule (use classical/critical value approach):
Test statistic and Analysis:
Conclusion:
p-value:
Explanation / Answer
Given that,
mean(x)=1114
standard deviation , s.d1=230
number(n1)=30
y(mean)=989
standard deviation, s.d2 =195
number(n2)=40
null, Ho: u1 = u2
alternate, the mean annual lease rate is higher in Hong Kong than in ParisH1: u1 > u2
level of significance, = 0.01
from standard normal table,right tailed t /2 =2.382
since our test is right-tailed
reject Ho, if to > 2.382
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (29*52900 + 39*38025) / (70- 2 )
s^2 = 44368.75
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=1114-989/sqrt((44368.75( 1 /30+ 1/40 ))
to=125/50.8741
to=2.457
| to | =2.457
critical value
the value of |t | with (n1+n2-2) i.e 68 d.f is 2.382
we got |to| = 2.457 & | t | = 2.382
make decision
hence value of | to | > | t | and here we reject Ho
p-value: right tail -ha : ( p > 2.457 ) = 0.00828
hence value of p0.01 > 0.00828,here we reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 2.457
critical value: 2.382
decision: reject Ho
p-value: 0.00828