Answer
There is a difference.
Work Step by Step
The sample size is more than 25, hence the value of the test statistic: $z=\frac{(x+0.5)-n/2}{\sqrt n/2}=\frac{(64+0.5)-82/2}{\sqrt{82}/2}=5.19.$ By using the table, the corresponding critical value: $z=\pm 1.96.$ If the value of the test statistic is in the rejection region, we reject the null hypothesis. 5.19 is more than 1.96 hence we reject the null hypothesis, hence there is a difference.
