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 :

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Answer:

The test statistic is [tex]Z = \frac{0.444-p_{0}}{\sqrt{p_{0}(1-p_{0})/1419}}[/tex] where [tex]p_{0}[/tex] 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 [tex]H_{0}: p = p_{0}[/tex] vs [tex]H_{1}: p > p_{0}[/tex], then the test statistic for this problem is given by [tex]Z = \frac{\hat{p}-p_{0}}{\sqrt{p_{0}(1-p_{0})/n}}[/tex]. We know that [tex]\hat{p} = 630/1419 = 0.444[/tex] and n = 1419, so [tex]Z = \frac{0.444-p_{0}}{\sqrt{p_{0}(1-p_{0})/1419}}[/tex].

A test statistic is a value derived from a statistical hypothesis test. The value of Z is  [tex]Z = \dfrac{0.444-p_0}{\sqrt{p_o(1-p_o)/1419}}[/tex].

What is test static?

A test statistic is a value derived from a statistical hypothesis test. It demonstrates how closely your observed data fit the anticipated distribution under the null hypothesis of the statistical test.

The p-value of your results is calculated using the test statistic, which aids in deciding whether to reject your null hypothesis.

Assume that p is the genuine fraction of the public who believes nuclear power plants are extremely/extremely dangerous to the environment and that we wish to test a hypothesis regarding p. Therefore, the test statistic can be written as,

[tex]Z = \dfrac{\hat{p}-p_0}{\sqrt{p_o(1-p_o)/n}}[/tex]

Now, we know the following values,

[tex]\hat p=\dfrac{630}{1419}=0.444[/tex] and n=1419, therefore, the value of Z can be written as,

[tex]Z = \dfrac{0.444-p_0}{\sqrt{p_o(1-p_o)/1419}}[/tex]

Hence, the value of Z is  [tex]Z = \dfrac{0.444-p_0}{\sqrt{p_o(1-p_o)/1419}}[/tex].

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