A certain real estate firm has appointed you to investigate the relationship between the median selling prices of houses and the average number of rooms per house in 506 districts of a large metropolitan area. The dependent variable is , the median selling price of a house in the district, measured in tens of thousands of shillings. The explanatory variable is , the average number of rooms per house in the district. The model you propose to estimate is given by the population regression equation

= 0 + 1 +

Your research assistant has used the 506 sample observations on and to estimate the following OLS sample regression equation, where the figures in parentheses below the coefficient estimates are the estimated standard errors of the coefficient estimates:

= -347.96+91.1955 + (i = 1, ..., n), n = 506 (26.52) (4.193) (standard errors)

i.) Compute and interpret the two-sided 95% confidence interval for the slope coefficient 1. [8 marks]

ii.) Perform a test of the null hypothesis 0: 1 = 0 against the alternative hypothesis 1: 1 0 at the 1% significance level. Show how you calculated the test statistic. State the decision rule you use, and the inference you would draw from the test. Briefly indicate the conclusion you would draw from the test. [8 marks]

iii.) Perform a test of the proposition that a one-room increase in average house size is associated on average with an increase in median house price of more than Sh. 800,000. Use the 5 percent significance level. State the null hypothesis and the alternative hypothesis. Show how you calculated the test statistic. State the decision rule you use, and the inference you would draw from the test. [8 marks]