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

Answer:

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

(2) Test statistic = 3.08

(3) P-value = 0.00104

Step-by-step 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. = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ 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  =  $\frac{0.54-0.50}{\sqrt{\frac{0.54(1-0.54)}{1475} } }$

                                    = 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.