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 correct analysis would be:
A) A sign test based on the binomial distribution
B) A sign test based on the standard normal distribution
C) A chi-square test
D) A Wilcoxon signed rank test

Question

Quizplus · Accepted Answer

The sign test based on the standard normal distribution is appropriate for this scenario because the sample size is small and the population distribution is unknown. The null hypothesis would be that the proportion of economists predicting an increase is equal to 0.50, and the alternative hypothesis would be that the proportion is greater than 0.50 (i.e. a one-tailed test). The test statistic would be calculated as the number of economists predicting an increase minus half the sample size, divided by the standard deviation of the sample proportion. If the test statistic falls above the 1.28 cutoff value for the 0.10 significance level, we would reject the null hypothesis and conclude that the majority of economists predict an increase in the economy.

20 Economists Were Sampled and Asked to Predict If the National