Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 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 null hypothesis is ________. A)H₀ : π = 0.5 B)H₀ : π ≠ 0.5 C)H₀ : π ≤ 0.5 D)H₀ : π ≥ 0.5

Question

Quizplus · Accepted Answer

The null hypothesis should be that the proportion of economists who predict an increase in the economy (π) is less than or equal to 0.5 (i.e., not a majority). Therefore, the correct null hypothesis is H₀ : π ≤ 0.5. This is a one-tailed test, because we are only interested in whether the proportion predicting an increase is less than 0.5, not whether it is significantly different from 0.5 in either direction. The significance level is given as 0.10, so we will reject the null hypothesis if our sample proportion of economists predicting an increase (p-hat) is less than the critical value for a one-tailed test with a 0.10 significance level.

Twenty Economists Were Sampled and Asked to Predict If the National