Question

Hypothesis: In a comparison of countries, those having economies less dependent on oil wealth will be more democratic than will countries having economies more dependent on oil wealth. Consider the following data, which present information for 20 countries with non-oil-dependent economies and fifteen countries with oil-dependent economies. The dependent variable is a 7-point level-of-democracy scale, with higher scores denoting more democracy.

Oil-dependent economy?                    Mean Democracy                   Standard Error

No                                                       4.7                                           0.51

Yes                                                      2.6                                           0.28

A. State the null hypothesis for the non-oil-dependent/oil-dependent comparison.

B. Calculate the difference between the means of the democracy scale for the two groups of countries. Calculate the standard error of the difference. Calculate the t-statistic. What is the p-value using a two-tailed test?

C. Suppose we have strong theoretical reasons for a one-tailed test. Is the difference statistically significant? Explain how you know.

D. Based on the results in parts B and C, suppose a researcher decides to reject the null hypothesis. Is this decision supported by the statistical evidence? Explain.

Explain.

Answer 1

a. State the null hypothesis for the non-oil-dependent/oil-dependent comparison.

i. There is no difference between non-oil dependent and oil-dependent democracy.

b. Answer the following:

i. Calculate the difference between the means of the democracy scale for non-oil-dependent and oil-dependent countries.

Calculate the standard error of the difference.

SE of Difference =

Calculate the t statistic

Based on these results, suppose a researcher decides to reject the null hypothesis. Is this decision supported by the statistical evidence? Explain.

The calculated value of t = 26.4484 is more dun the table value of t = 1.96. Therefore, we reject the null hypothesis and the decision of the researcher to do so is supported by the statistical evidence.