Question

A recent Quinnipiac University Poll (conducted January 8-12, 2020) surveyed 1,562 registered voters nationwide. Respondents were asked, “Are you troubled by President Trump’s actions involving Ukraine, or not?”. Of those surveyed, 812 said that they are troubled.

Research hypothesis: More than half (i.e., 50%) of registered voters nationwide are troubled by President Trump’s actions involving Ukraine.

1. Explain why it is fair to use normal theory methods in this case to find the standard error (and then the margin of error). (1 pt)

2. Find the margin of error using normal theory methods. (2 pts)

3. Does the data support the research hypothesis? Can we conclude that more than half of registered voters nationwide are troubled by President Trump’s actions involving Ukraine? Explain why or why not. Write a paragraph to summarize your conclusions, addressing both the p-value and your confidence interval in your discussion. (2 pts)

Answer 1

n*p = 1562*0.5 > 10

n*(1 - p) = 1562*(1 - 0.5) > 10

We can use the normal theory model.

p̂ = 812/1562 = 0.5198

Standard error = √p(1-p)/n = √0.50(1-0.50)/1562 = 0.0127

Margin of error = z*√p(1-p)/n = 1.96*√0.50(1-0.50)/1562 = 0.0248

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.5198 - 0.50)/√0.50(1-0.50)/1562

z = 1.57

The hypothesis being tested is:

H₀: p = 0.50

H_a: p > 0.50

The p-value for z = 1.57 is 0.0584.

Since the p-value (0.0584) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that more than half of registered voters nationwide are troubled by President Trump’s actions involving Ukraine.