Question

Assume that adults were randomly selected for a poll. They were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of those polled, 486 were in favor, 397 were opposed, and 118 were unsure. A politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 118 subjects who said that they were unsure, and use a 0.01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the politician's claim?

Part A) Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A. H₀: p = 0.5, H₁: p > 0.5

B. H₀: p = 0.5, H₁: p ≠ 0.5

C. H₀: p ≠ 0.5, H₁: p = 0.5

D. H₀: p = 0.5, H₁: p < 0.5

Part B) identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

(Round to two decimal places as needed.)

Part D) Identify the P-value for this hypothesis test.

The P-value for this hypothesis test is

(Round to three decimal places as needed.)

Identify the conclusion for this hypothesis test.

A. Reject H₀. There is sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

B. Fail to reject H0 . There is not sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

C. Fail to reject H₀ There is sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

D. Reject H₀. There is not sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

What does the result suggest about the politician's claim?

A. The result suggests that the politician is correct in claiming that the responses are random guesses equivalent to a coin toss.

B. The result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss.

C. The result suggests that the politician is doing his best to accurately portray the feelings of the people.

D. The results are inconclusive about whether the politician is correct or not.

Answer 1

The statistical software output for this problem is:

Hence,

Part - A) Hypotheses:

H₀: p = 0.5, H₁: p ≠ 0.5

Option B is correct.

Part - B) Test statistic = 3.00

Part - D) p - Value = 0.003

Conclusion: Reject H₀. There is sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss. Option A is correct.

What does the result suggest about the politician's claim?

The result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss. Option B is correct.