Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes?
A) reject
B) accept

Question

Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? ​
A) reject
B) accept

Quizplus · Accepted Answer

The sample size is large enough to use the normal distribution to approximate the binomial distribution. The sample proportion of workers opposed to the increase in taxes is 53/80 = 0.6625. The standard deviation of the sample proportion is sqrt(0.6625 * 0.3375 / 80) = 0.0433. The z-score for the sample proportion is (0.6625 - 0.5) / 0.0433 = 3.78. The p-value for the z-score is less than 0.0001, which is less than the significance level of 0.05. Therefore, we reject the hypothesis that the majority of workers are opposed to the increase in taxes.

Suppose That of 80 Workers Randomly Selected and Interviewed, 53