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 $1,118 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 $985 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.)

a. H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

b. H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

    

c.H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

d. H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ = 0

e. H₀: μ₁ − μ₂ > 0

H_a: 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.)

Use α = 0.01. What is your conclusion?

a. 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.

b. 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.    

c. 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.

d. There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.

Answer 1

Answer)

Null hypothesis Ho : u1 - u2 <= 0

Alternate hypothesis Ha : u1 - u2 > 0

Test statistics t = (x1-x2)/(standard error)

Standard error = √{(s1^2/n1)+(s2^2/n2)}

X1 = 1118, S1 = 230, N1 = 30

X2 = 985, S2 = 195, N2 = 40

After substitution

Test statistics t = 2.553

Degrees of freedom is = smaller of n1-1, n2-1 = 29

For 29 dof and 2.553 test statistics, P-value from t distribution is = 0.0081

Since the obtained p-value is less than the given significance 0.01

There is sufficient evidence to conclude that the mean annual lease rate is higher in the Asian city than in the European City.