Question

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

Answer 1

Answer:

1) Null hypothesis:$p\leq 0.5$  

Alternative hypothesis:$p > 0.5$  

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

2) $z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1475}}}=3.072$  

3) $p_v =P(z>3.072)=0.00106$  

4) The p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v$ 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

$\hat p=0.54$ estimated proportion of adults who think the Civil War is still relevant to American politics and political life

$p_o=0.5$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

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

Null hypothesis:$p\leq 0.5$  

Alternative hypothesis:$p > 0.5$  

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:  

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

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

Calculate the statistic  

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

$z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1475}}}=3.072$  

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 $\alpha=0.1$. The next step would be calculate the p value for this test.  

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

$p_v =P(z>3.072)=0.00106$  

So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis

B. Reject H_0