20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The test statistic is:
A) 0.707
B) 1.179
C) 1.707
D) 0.179

Question

Quizplus · Accepted Answer

To test the hypothesis, we will use a one-sample proportion test with the null hypothesis being that the proportion of economists predicting an increase is equal to 0.5 and the alternative hypothesis being that the proportion is greater than 0.5.

Let p be the sample proportion of economists predicting an increase, which is 11/20 = 0.55.
The test statistic is:

z = (p - 0.5) / sqrt(0.5 * 0.5 / 20) = 0.707

The p-value for this test is P(Z > 0.707) = 0.24.
Since the p-value is greater than the significance level of 0.10, we fail to reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the majority of economists predict an increase in the national economy.

20 Economists Were Sampled and Asked to Predict If the National