Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly different from 0.36. With H1 : p ≠ 0.36 you obtain a test statistic of z = 2.074 . Use a normal distribution calculator and the test statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.

Answer 1

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:

Null hypothesis:
`p=0.36`

Alternative hypothesis:
`p \\eq 0.36`

Since is a bilateral test the p value would be:

`p_v =2*P(z>2.074)=0.0381`

Explanation:

Data given and notation n

n represent the random sample taken

`\hat p` estimated proportion of interest

`p_o=0.36` is the value that we want to test

z would represent the statistic (variable of interest)

`p_v` represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:

Null hypothesis:
`p=0.36`

Alternative hypothesis:
`p \\eq 0.36`

When we conduct a proportion test we need to use the z statisitc, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic

For this case the statistic is given:

`z = 2.074`

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

`p_v =2*P(z>2.074)=0.0381`