Question

Commercial real estate prices and rental rates suffered substantial declines in the past year (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 in many cities in Europe and the United States. Annual lease rates for a sample of 30 commercial properties in Hong Kong showed an average of $1114 per square meter with a standard deviation of $230. Annual lease rates for a sample of 40 commercial properties in Paris showed an average 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 Hong Kong than in Paris? Develop appropriate null and alternative hypotheses.

b. Use α = 0.01. What is your conclusion?

c. Are rental rates higher in Hong Kong than in Paris?

Answer 1

a) Null hypothesis H₀ : There is no difference between rental rates of Hong Kong and Paris.

Alternative hypothesis H₁:

The rental rates is higher in Hong Kong than in Paris

That is H₁ :x₁⁻ > x₂⁻

b) By tabulated value z = 2.58 at 0.01 level of significance

c) the null hypothesis is accepted.

Rental rates are not higher in Hong Kong than in Paris?

Explanation:

Step 1:-

Annual lease rates for a sample of 30 commercial properties

size of the sample n₁ = 30

Given data in Hong Kong Annual lease rates of showed an average of $1114 per square meter with a standard deviation of $230.

sample mean x₁⁻ = $1114

sample standard deviation σ₁ = 230

Given data Annual lease rates for a sample of 40 commercial properties in Paris showed an average lease rate of $989 per square meter with a standard deviation of $195.

Size of second sample n₂ =40

mean of the second sample x₂⁻ = $989 per square meter

sample standard deviation σ₂ = 195

Step 2:-

Null hypothesis H₀ : There is no difference between rental rates of Hong Kong and Paris.

Alternative hypothesis H₁:

The rental rates is higher in Hong Kong than in Paris

That is H₁ :x₁⁻ > x₂⁻

Level of significance:α = 0.01

Step 3:-

The test statistic Z =
`\frac{x^(-) _(1)-x^(-) _(2) }{\sqrt{( σ₁^2)/(n_(1) )+( σ^2_(2) )/(n_(2) ) } }`

now substitute values σ₁ = 230 , σ₂ = 195 , n₁ = 30 and n₂ =40

Z = 2.39

on calculation we get Z = 2.39

By tabulated value z = 2.58 at 0.01 level of significance

Z = 2.39< 2.58

Therefore the null hypothesis is accepted.

Rental rates are not higher in Hong Kong than in Paris?

Final answer :-

a) Null hypothesis H₀ : There is no difference between rental rates of Hong Kong and Paris.

Alternative hypothesis H₁:

The rental rates is higher in Hong Kong than in Paris

That is H₁ :x₁⁻ > x₂⁻

b) By tabulated value z = 2.58 at 0.01 level of significance

c) the null hypothesis is accepted.

Rental rates are not higher in Hong Kong than in Paris?