Question

A national survey conducted among a simple random sample of 1513 adults shows that 835 of Americans think the Civil War is still relevant to American politics and the political life.

Conduct a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant. Give answers to at least 4 decimal places.

A)Identify the claim

B)What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)
H0:
H1:

C)What test should you run?
2-propZInt
2-propZTest
1-propZTest
1-propZInt

D)Check the conditions for the test are satisfied.

E)Based on the hypotheses, find the following to at least 4 decimal places:

Test Statistic =
p-value =

F)Based on the above we choose to
Accept the null hypothesis
Reject the null hypothesis
Fail to reject the null hypothesis
Accept the alternative hypothesis
G)Interpret your final conclusion in nontechnical terms and address the original claim.

2.Calculate a 95% confidence interval for the proportion of Americans who think the Civil War is still relevant. Give your answer to at least 4 decimal places.

A)Interpret the interval in this context.

B)Does the confidence interval agree with the conclusion of the hypothesis test?

Answer 1

a)

claim is the majority of the Americans think the Civil War is still relevant

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.5
Alternative Hypothesis, Ha: p > 0.5

c)
1-propZTest

d)
The sample must be reasonably random
• The sample must be less than 10% of the population
• The sample must be large enough so that:
n• pˆ and n(1 - pˆ ) ≥ 10 for a confidence interval
n• p and n(1 - p) ≥ 10 for the significance test

e)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.5519 - 0.5)/sqrt(0.5*(1-0.5)/1513)
z = 4.0375

P-value Approach
P-value = 0

f)

As P-value < 0.05, reject the null hypothesis.

g)
There is sufficient evidence to conclude that the majority of the Americans think the Civil War is still relevant

2)

sample proportion, = 0.5519
sample size, n = 1513
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.5519 * (1 - 0.5519)/1513) = 0.0128

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0128
ME = 0.0251

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.5519 - 1.96 * 0.0128 , 0.5519 + 1.96 * 0.0128)
CI = (0.5268 , 0.577)

We are 95% confident that te proportion is between (0.5268 , 0.577)

b)

yes