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, 481 were in​ favor, 397 were​ opposed, and 120 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 120 subjects who said that they were​ unsure, and use a 0.05 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?

1. Identify the null and alternative hypotheses for this test. Choose the correct answer below.

H0 : p = 0.5

H1 : p =/ 0.5

2. Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is _______ (Round to two decimal places as​ needed.)

3. Identify the P value for this hypothesis test.

The P-value for this hypothesis test is _________ (Round to two decimal places as​ needed.)

4. Identify the conclusion for this hypothesis test.

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

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

5. What does the result suggest about the​ politician's claim?

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

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

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

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

Please, include all the steps to get the answers. I am having a hard time understanding this problem on my own. Thank you in advance!

Answer 1

Sample size, n = 481+397 = 878  
People in favor, x = 481  
Sample proportion, p̄ = x/n = 481/878 = 0.5478
α =    0.05  
  
1. Null and Alternative hypothesis:      
Ho : p =   0.5  
H1 : p ≠   0.5  
            
2. Test statistic:      

3. p-value = 2*(1-NORM.S.DIST(2.83, 1)) = 0.0046

4. Conclusion: As p-value = 0.0046 <0.05, we reject Ho.

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

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