# Chapter 13 - Nonparametric Statistics - 13-2 Sign Test - Basic Skills and Concepts: 16

There is a difference.

#### Work Step by Step

The sample size is more than 25, hence the value of the test statistic: $z=\frac{(x+0.5)-n/2}{\sqrt n/2}=\frac{(242+0.5)-396/2}{\sqrt{396}/2}=4.47.$ 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. 4.47 is less than 1.96 hence we reject the null hypothesis, hence there is a difference.

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