Question

20. Stem Cell Survey Adults were randomly selected for a Newsweek poll. They were asked if they “favor or oppose using federal tax dollars to fund medical research using stem cells ob- tained from human embryos.” Of those polled, 481 were in favor, 401 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 0.01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result sug- gest about the politician’s claim?

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.50
Alternative hypothesis: P 0.50

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.01677
z = (p - P) /S.D

z = 2.70

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -2.70 or greater than 2.70.

Thus, the P-value = 0.007

Interpret results. Since the P-value (0.007) is less than the significance level (0.01), we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the proportion of subjects who respond in favor is equal to 0.5.