Answer
there is a difference.
Work Step by Step
The sample size is more than 25, hence the value of the test statistic: $z=\frac{(x+0.5)-n/2}{\sqrt n/2}=\frac{(239+0.5)-291/2}{\sqrt{ 291}/2}=11.02.$ 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. 11.02 is more than 2.575 hence we reject the null hypothesis, hence there is a difference.
