To determine whether a single coin is fair, the coin was tossed 250 times, and heads was observed 140 times. What is the value of the test statistic?
A) 13.6
B) 30
C) 40
D) 110

Question

Quizplus · Accepted Answer

We need to conduct a one-sample proportion test. The null hypothesis is H0: p = 0.5 (the coin is fair), and the alternative hypothesis is Ha: p ≠ 0.5 (the coin is not fair). The test statistic is calculated as (phat - p) / sqrt(pq/n), where phat is the sample proportion (140/250 = 0.56), p is the hypothesized proportion under the null hypothesis (0.5), q is 1-p (0.5), and n is the sample size (250). Plugging in the values gives us (0.56 - 0.5) / sqrt(0.5*0.5/250) = 2.73, which corresponds to a p-value of 0.006. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the coin is not fair. The closest answer choice to the calculated test statistic is A) 13.6.

To Determine Whether a Single Coin Is Fair, the Coin