Amember of the house of representatives wants to determine the proportion of voters in her district who favor a flat income tax. a random sample of 200 voters in her district showed 89 in favor. (brase & brase, understandable statistics, test item file p.8-4).a. is there evidence at the 5% level that the majority of voters oppose the tax?

If we compare the p value obtained with the significance level given we see that so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of voters in her district who oppose a flat income tax is not significantly higher than 0.5 or 50%.  

Step-by-step explanation:

1) Data given and notation

n=200 represent the random sample taken

X=89 represent the voters in her district who favor a flat income tax

estimated proportion of voters in her district who oppose a flat income tax

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the majority of voters oppose the tax:  

Null hypothesis:  

Alternative hypothesis:  

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

(1)  

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

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

4) 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 significance level provided . The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

If we compare the p value obtained with the significance level given we see that so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of voters in her district who oppose a flat income tax is not significantly higher than 0.5 or 50%.  

answer: -8.2562234e+13