A property agent carries out a study on the relationship between the age of a building and the maintenance costs, X, per square metre per annum based on a sample of 86 buildings. In the sample denote...

A property agent carries out a study on the relationship between the age of a building and the maintenance costs, X, per square metre per annum based on a sample of 86 buildings. In the sample denote by xi the annual maintenance costs per square metre for building i. The maintenance costs are summarised in the following table:
sample size new buildings 35 old buildings 61
? xi 100 300
? x2i 800 2200
(a) Perform a test for the null hypothesis that the variance of the maintenance costs of
new buildings is equal to the variance of the maintenance costs for old buildings,
against the alternative that the variance of the maintenance costs of new buildings
is larger. Use a significance level of 5%. (6)
(b) Perform a test of the null hypothesis that the mean of the maintenance costs of new buildings is equal to the mean of the maintenance costs for old buildings, against
the alternative of different means. Use a significance level of 5%