Answer:
(1) : p = 0.5,
: 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, : p = 0.50 {means that 50% of the Americans think that the Civil War is still relevant}
Alternate Hypothesis, : 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. = ~ N(0,1)
where, = % 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, <u>test statistics</u> =
= 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 3.08) {using z table}
= 1 - 0.99896 = 0.00104
So, the p-value for this hypothesis test is 0.00104.