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, 487 were in​ favor, 402 were​ opposed, and 122 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 122 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? Identify the null and alternative hypotheses for this test. Choose the correct answer below.

Answer 1

ANSWER -

We can use a hypothesis test to assess whether the politician's claim that people's responses to the stem cell issue are equivalent to a coin toss is supported by the data. We will exclude the 122 subjects who were unsure, as their responses do not provide information about their position on the issue.

The null hypothesis for this test is that the proportion of adults who favor using federal tax dollars to fund stem cell research is equal to 0.5, which is the same as the proportion who would respond randomly to the question. The alternative hypothesis is that the proportion who favor or oppose stem cell research is different from 0.5.

We can perform a one-sample proportion test using the following formula:

z = (p - P) / sqrt(P(1-P) / n)

where p is the sample proportion, P is the hypothesized proportion (0.5), and n is the sample size (487 + 402 - 122 = 767). The resulting test statistic, z, can be compared to the standard normal distribution to determine the p-value.

Plugging in the values, we get:

p = 487 / (487 + 402) = 0.548
z = (0.548 - 0.5) / sqrt(0.5 * 0.5 / 767) = 2.43
p-value = P(Z > 2.43) = 0.0076 (using a one-tailed test)

Using a significance level of 0.05, we can reject the null hypothesis because the p-value is less than 0.05. This means that the proportion of adults who favor stem cell research is significantly different from 0.5 and that the politician's claim that people's responses are random is not supported by the data.

Therefore, we can conclude that there is evidence to suggest that people have an opinion on the stem cell issue and that their responses are not equivalent to a coin toss.