Question

The Civil War. Suppose a national survey conducted among a simple random sample of 1520 American adults, 825 indicate that they 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 the majority (more than 50%) of Americans think the Civil War is still relevant.

A. H0:p=0.5H0:p=0.5, HA:p≠0.5HA:p≠0.5
B. H0:p=0.5H0:p=0.5, HA:p>0.5HA:p>0.5
C. H0:p=0.5H0:p=0.5, HA:p<0.5HA:p<0.5

2. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.

4. Based on the p-value, we have:

Answer 1

1)

H0: p = 0.50 , Ha: p > 0.50

2)

Sample proportion $\hat{p}$ = 825 / 1520 = 0.5428

Test statistics = $\hat{p}$ - p / sqrt [ p (1 - p) / n]

= 0.5428 - 0.50 / sqrt [ 0.50 * 0.50 / 1520 ]

= 3.34

3)

p-value = P(Z > z)

= P(Z > 3.34)

= 0.0004

4)

At 0.05 significance level, since p-value < 0.05 level, Reject H0