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, 488 were in​ favor, 399 were​ opposed, and 121 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 121 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?

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

A.

Upper H 0​: p = 0.5

Upper H 1​: p < 0.5

B.

Upper H 0​: p = 0.5

Upper H 1​: p ≠ 0.5

C.

Upper H 0​: p ≠ 0.5

Upper H 1​: p = 0.5

D.

Upper H 0​: p = 0.5

Upper H 1​: p > 0.5

Identify the test statistic for this hypothesis test. ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test. ​(Round to three decimal places as​ needed.)

Identify the conclusion for this hypothesis test.

A. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

B. Reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

C. Fail to reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

D. Fail to reject Upper H 0. There is 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 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 correct in claiming that the responses are random guesses equivalent to a coin toss.

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

Answer 1

We have to exclude 121, so we left with 488 votes in favor and 399 votes opposed

total = 488+399 = 887

So, proportion for favor = (number of votes in favor)/(total number of votes) = 488/887 = 0.55

sample proportion

population proportion po = 0.50

we need to test the claim whether the proportion of subjects who responded in favor is equal to 0.50 or not. So, it is two tailed hypothesis because the proportion of subjects who responded in favor might be less or greater than 0.50

So, we assume that the proportion is equal to 0.50 for null hypothesis and we will test it as not equal to 0.50 for alternate hypothesis

So, the following hypothesis needs to be tested

Option B is correct for hypothesis

Calculation for test statistic

we have to use z test statistic here because this is a case of proportion.

Formula for the test statistic is given as

where we have

setting the given values, we get

Now using the z distribution, looking 2.9 in column then 0.08 in row to get the p value for the two tailed test, we get

p value = 0.0029, which is less than 0.01, so it is significant.

we can reject the null hypothesis because result is significant.

we can conclude that there is enough evidence to warrant the rejection of claim that the responses are equivalent to coin toss.

option A is correct.

Since the claim is incorrect, so we can say that the result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss

So, option D is correct.