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,

483483

were in​ favor,

402402

were​ opposed, and

115115

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

115115

subjects who said that they were​ unsure, and use a

0.010.01

significance level to test the claim that the proportion of subjects who respond in favor is equal to

0.50.5.

What does the result suggest about the​ politician's

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 = 0.0168
z = (p - P) /S.D

z = 2.72

z_{Critical =}+ 2.576

Rejection region is - 2.576 > z > 2.576

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 - 2.72 or greater than 2.72.

P-value = P(z < - 2.72) + P(z > 2.72)

Use z-calculator to find the p-values.

P-value = 0.0033 + 0.0033

Thus, the P-value = 0.0066.

Interpret results. Since the P-value (0.0066) is less than the significance level (0.01), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the proportion of subjects who respond in favor is equal to 0.50.