A recent study by the World Bank wished to determine whether there was a relatio

Question

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

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 Blank 3
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. _______

Explanation / Answer

1) H0: The slope of the regression line is equal to zero.
    Ha: The slope of the regression line is not equal to zero

Ans) ne

2) We get the slope (b1) and the standard error (SE) from the regression output.

b1 = -0.0048      SE = 0.0029

Test stat t = b1/SE = -0.0048/0.0029 = -1.66

3) Degrees of Freedom = n - 2 = 40 - 2 = 38

   critical value (in absolute terms) for alpha = 0.05 and df = 38 is 2.024

4) The rejection area is t < - 2.024 or t > +2.024

Since test stat does not lie in the rejection region we fail to reject the Null

Ans) No

5) No

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