Question

In 1993, the General Social Survey included a question that asked its participants if they felt that nuclear power plants were extremely/very dangerous to the environment. Out of the 1419 surveyed, 630 said yes. What is the value of the test statistic for this problem?

Answer 1

Answer:

The test statistic is $Z = \frac{0.444-p_{0}}{\sqrt{p_{0}(1-p_{0})/1419}}$ where $p_{0}$ is a fixed number.

Step-by-step explanation:

If we suppose that p is true proportion of people in the entire population who thinks that nuclear power plants were extremely/very dangerous to the enviroment, and we want to test a hypothesis about p, for instance $H_{0}: p = p_{0}$ vs $H_{1}: p > p_{0}$, then the test statistic for this problem is given by $Z = \frac{\hat{p}-p_{0}}{\sqrt{p_{0}(1-p_{0})/n}}$. We know that $\hat{p} = 630/1419 = 0.444$ and n = 1419, so $Z = \frac{0.444-p_{0}}{\sqrt{p_{0}(1-p_{0})/1419}}$.