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 \\eq 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

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{(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<\alpha` so we can conclude that we have enough evidence to reject the null hypothesis

B. Reject H_0

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{(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{(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<\alpha` so we can conclude that we have enough evidence to reject the null hypothesis

B. Reject H_0