The Civil War. Suppose a national survey conducted among a simple random sample of 1475 adults shows that 54% of Americans think the Civil War is still relevant to American politics and political life. Round all results to four decimal places.

1. What are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant.

A. H_0: p = 0.5, H_A: p > 0.5
B. H_0: p = 0.5, H_A: p < 0.5
C. H_0: p = 0.5, H_A: p \neq 0.5
2. Calculate the test statistic for this hypothesis test. =
3. Calculate the p-value for this hypothesis test.
4. What is your conclusion using \alpha = 0.1?
A. Do not reject H_0
B. Reject H_0

1) Null hypothesis:  

Alternative hypothesis:  

A. H_0: p = 0.5, H_A: p > 0.5

2)  

3)  

4) The p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis

B. Reject H_0

Step-by-step explanation:

Data given and notation

n=1475 represent the random sample taken

estimated proportion of adults who think the Civil War is still relevant to American politics and political life

is the value that we want to test

represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

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 majority of Americans think the Civil War is still relevant to American politics and political life.:  

Null hypothesis:  

Alternative hypothesis:  

A. H_0: p = 0.5, H_A: p > 0.5

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 .

Calculate the statistic  

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

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:  

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis

B. Reject H_0