Elementary Statistics (12th Edition)

The number of correct guesses can be obtained by multiplying the percentage and the sample size: $0.55 \cdot 144=57.2\approx57.$ The sample size is more than 25, hence the value of the test statistic: $z=\frac{(x+0.5)-n/2}{\sqrt n/2}=\frac{(57+0.5)-104/2}{\sqrt{104}/2}=1.08.$ By using the table, the corresponding critical value: $z=\pm 2.575.$ If the value of the test statistic is in the rejection region, we reject the null hypothesis. 1.08 is between -1.96 and 1.96 hence we fail to reject the null hypothesis, hence there is no difference.