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

The p-value obtained is less than the significance level at which the test was performed, so, we reject the null hypothesis & accept the alternative hypothesis and conclude that there is enough evidence to suggest that the proportion of subjects who respond in favor of using federal tax dollars to fund medical research using stem cells obtained from human​ embryos is NOT equal to 0.5

Therefore, the politician's claim is untrue.

Explanation:

For hypothesis testing, we first clearly state our null and alternative hypothesis.

The null hypothesis is that the proportion of subjects who respond in favor of using federal tax dollars to fund medical research using stem cells obtained from human​ embryos is equal to 0.5.

And the alternative hypothesis is that the proportion of subjects who respond in favor of using federal tax dollars to fund medical research using stem cells obtained from human​ embryos is not equal to 0.5.

Mathematically, the null hypothesis is

H₀: p₀ = 0.50

The alternative hypothesis is

Hₐ: p₀ ≠ 0.50

To do this test, we will use the z-distribution

So, we compute the z-test statistic

z = (x - μ)/σₓ

x = the proportion of people in favour of using federal tax dollars to fund medical research using stem cells obtained from human​ embryos = p = 487 ÷ (487+402) = 0.548 (excluding the 122 people unsure)

μ = p₀ = 0.50

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 487 + 402 = 889 (excluding the 122 people unsure)

σₓ = √[0.548×0.452/889] = 0.0166920092 = 0.01669

z = (0.548 - 0.50) ÷ 0.01669

z = 2.88

checking the tables for the p-value of this z-statistic

p-value (for z = 2.88, at 0.05 significance level, with a two tailed condition) = 0.003977

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 5% = 0.05

p-value = 0.003977

0.003977 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis & accept the alternative hypothesis and conclude that there is enough evidence to suggest that the proportion of subjects who respond in favor of using federal tax dollars to fund medical research using stem cells obtained from human​ embryos is NOT equal to 0.5

The politician's claim is untrue.

Hope this Helps!!!