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,490 were in​ favor,396 were​ opposed, and 117 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 117 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?

Answer 1

Let the proportion, p = number of adults who favor using federal tax dollars to fund medical research using stem cells obtained from human​embryos

Proportion, p, follows the normal distribution.

The null and alternative hypotheses are defined as,

The z-statistic is obtained using the formula,

Where,

The p-value is obtained from z-distribution table for z = 3.158

Since the P-value is 0.0016<0.05 at 5% significant level, the null hypothesis is rejected. Hence we can conclude that there is a significant difference between the proportion who favor and who oppose of using federal tax dollars to fund medical research using stem cells obtained from human​embryos.