Question

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.T 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 $1,116 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 $989 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 u, population mean annual lease rate per square meter in the Asian city and u,= population mean annual lease rate per square meter in the European city.) Ho H-H2o Ho:41-20 O Ho -20 H -20 O Ho H-H20 Ho -20 H -20 (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.) 0.01. What is your conclusion? Use a Reject Ho. 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 Ho There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City. ODo not reject Ho. There is insufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City Reject Ho There is insufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City

Answer 1

(a) Ho 120 Ha 2 0 (b)

Test for Two Variances

Method

Null hypothesis         Sigma(1) / Sigma(2) = 1
Alternative hypothesis Sigma(1) / Sigma(2) not = 1
Significance level      Alpha = 0.01

Statistics

Sample            N    StDev   Variance
Asian city        30 230.000 52900.000
European city 40 195.000 38025.000

Ratio of standard deviations = 1.179
Ratio of variances = 1.391

Tests

                                  Test
Method           DF1 DF2 Statistic P-Value
F Test (normal)   29   39       1.39    0.333

Hence we can assume that two population variances are same.

Two-Sample T-Test and CI

                          SE
Sample           N Mean StDev Mean
Asian city     30 1116    230    42
European city 40   989    195    31

Difference = mu (1) - mu (2)
Estimate for difference: 127.0

Difference Test statistic 2.496 1 1 + 40 30 where, p value Since p value< 0.01 so Reject Ho. There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the Europian City = pooled sd P(t> 2.496lt 210.6389 S t68)0.0075.