Question

Twenty economist were chosen randomly, and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an improvement, and nine economists predicted a decrease in the economy. Conduct a hypothesis test to determine if there is a difference in the prediction for the national economy during the next 12 months. Use the normal approximation to the Binomial. In addition, assign a “+” sign to “Improvement” and a “-” sign to “Decrease.” Conduct a two-tailed test at the .05 significance level. Based on the analysis, what is your conclusion?

Answer 1

Given that, Twenty economist were chosen randomly, and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an improvement, and nine economists predicted a decrease in the economy. That is, n1 = n2 = 20 , x1 = 11 and x2 = 9

The null and the alternative hpotheses are,

Test statistic is, Z = 0.63

since, it is two tailed test,

p-value = 2 * P(Z > 0.63) = 2 * 0.2643 = 0.5286

p-value = 0.5286

Here, p-value = 0.5286 > significance level = 0.05

so, we fail to reject the null hypothesis.

Conclusion: There is not sufficient evidence to conclude that there is a difference in the prediction for the national economy during the next 12 months. That is there is no difference between them.