In: Statistics and Probability
You may need to use the appropriate technology to answer this question. Commercial real estate prices and rental rates suffered substantial declines in 2008 and 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 an Asian city 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 a European city showed a mean lease rate of $987 per square meter with a standard deviation of $195.
(a) On the basis of the sample results, can we conclude that the mean annual lease rate is higher in the Asian city than in the European City? Develop appropriate null and alternative hypotheses. (Let μ1 = population mean annual lease rate per square meter in the Asian city and μ2 = population mean annual lease rate per square meter in the European city.)
H0: μ1 − μ2 ≠ 0
Ha: μ1 − μ2 = 0
H0: μ1 − μ2 > 0
Ha: μ1 − μ2 ≤ 0
H0: μ1 − μ2 ≤ 0
Ha: μ1 − μ2 = 0
H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
H0: μ1 − μ2 ≤ 0
Ha: μ1 − μ2 > 0
(b)What is the value of the test statistic? (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
(c) Use α = 0.01. What is your conclusion?
Do not reject H0. There is insufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.
Reject H0. There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.
Do not Reject H0. There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.
Reject H0. There is insufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.
Ans.
Note :- We find Test Statistics and p-value using MINiTAB
Steps:-
1 Choose Stat > Basic Statistics > 2-Sample t.
2 Summarized data: Choose if you have summary values for the sample size, mean, and standard deviation for each sample.
First
Sample size: Enter the value for the sample size.
Mean: Enter the value for the mean.
Standard deviation: Enter the value for the standard deviation.
Second
Sample size: Enter the value for the sample size.
Mean: Enter the value for the mean.
Standard deviation: Enter the value for the standard deviation.
Assume equal variances: Check to assume that the populations have equal variances. The default is to assume unequal variances.
We assume Population Variances are not equal:-
(b) Test Statistics:-
t = 2.438
P-value:-
P-value = 0.0090
(c)
Reject H0. There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.