QUESTION 1

A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 40 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of b₀ and b₁ are reported in parentheses below the coefficients of b₀ and b₁

Y = 5.358 - 0.0048 X

(1.380) (0.0029)

To test the significance of the relationship, a 5% level of significance was adopted.

1. State the direction of the alternative hypothesis used to test the statistical significance of the relationship. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 

2. Calculate the test statistic, reporting your answer to two decimal places. 

3. Use the tables in the textbook to determine the critical value (in absolute terms) to three decimal places 

4. Is the null hypothesis rejected for this test? Type yes or no. 

5. Disregarding your answer in part 4, if the null hypothesis was not rejected, would there appear to be a linear relationship between resource abundance and economic growth? Type yes or no. 

QUESTION 2

The Maroochy Chamber of Commerce is interested in determining the relationship between the number of fine days each year and the number of interstate and overseas tourists visiting the Sunshine Coast each year, measured in thousands. Using annual data from 1993 to 2005 (inclusive), the following model was estimated: Y = -5.29 + 0.69 X 

Error sum of squares: 319       Sum of squares of X: 903

Determine the upper limit for the 90% confidence interval for the slope correct to two decimal places.