Question

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 =/ 0.5
2. Calculate the test statistic for this hypothesis test.
3. Calculate the p-value for this hypothesis test.

Answer 1

(1)
`H_0` : p = 0.5,
`H_A` : p > 0.5

(2) Test statistic = 3.08

(3) P-value = 0.00104

Explanation:

We are given that 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.

We have to test the hypothesis to determine if there is a strong evidence that the majority of the Americans think the Civil War is still relevant.

(1) Let Null Hypothesis,
`H_0` : p = 0.50 {means that 50% of the Americans think that the Civil War is still relevant}

Alternate Hypothesis,
`H_a` : p > 0.50 {means that majority of the Americans think that the Civil War is still relevant,i.e; more than 50%}

The test statistics that will be used here is One-sample proportion test;

T.S. =
`\frac{\hat p -p}{\sqrt{(\hat p(1-\hat p))/(n) } }` ~ N(0,1)

where,
`\hat p` = % of Americans who think that the Civil War is still relevant in a sample of 1475 adults = 54%

p = population proportion

n = sample of american adults = 1475

(2) So, test statistics =
`\frac{0.54-0.50}{\sqrt{(0.54(1-0.54))/(1475) } }`

= 3.08

The value of test statistic for this hypothesis test is 3.08.

(3) P-value is given by the following situation;

P(Z > 3.08) = 1 - P(Z
`\leq` 3.08) {using z table}

= 1 - 0.99896 = 0.00104

So, the p-value for this hypothesis test is 0.00104.