Question

Does the data support the hypothesis that more than half of the countries in the world are mostly christian at the .05 significance level? How about at the .10 significance level?

Chrisitan	18
Orthodox	3
Muslim	1
Catholic	2
Jewish	1
Buddhist	2
Lutheran	3

Total = 30

Answer 1

Null Hypothesis H0: Proportion of the countries in the world that are mostly christian is less than or equal to 0.5. That is p 0.5

Alternative Hypothesis Ha: Proportion of the countries in the world that are mostly christian is greater than 0.5. That is p > 0.5

Standard error of sample proportion, SE = = = 0.09128709

Sample proportion, = 18/30 = 0.6

Test statistic, z = ( - p) / SE = (0.6 - 0.5) / 0.09128709 = 1.095

P-value = P(z > 1.095) =  0.1368

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence from the data that the true proportion of the countries in the world that are mostly christian is greater than 0.5.