Complete Question
Question 5
Suppose that in a poll, a random sample of U. S. adults were asked if they favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos. Further suppose that a certain politician criticizes the poll, saying that people don't really understand the stem cell issue, and that their responses are the equivalent of tossing a fair coin.
Express in symbolic form the null and alternative hypotheses needed to test the politician's claim. Define a "success" as a participant responding that they support funding.
A [tex]H_o: p=0.5\ \ H_A: p = 0.5[/tex]
B [tex]H_o: p=0.5 \ \ H_A: p\ne 0.5[/tex]
C [tex]H_o: p = 0.5 \ \ H_A:p \ge 0.5[/tex]
D [tex]H_o: p = 0.5 \ \ H_A: p < 0.5[/tex]
Question 6
For the hypothesis test in Problem 5, suppose that of those polled, 488 were in favor of funding medical research using stem cells obtained from human embryos, 405 were against, and 115 were unsure. Excluding the 115 participants who said they were unsure, calculate the resulting p-value. Round your answer to three decimal places; add trailing zeros as needed.
Answer:
Question 5
The correct option is B
Question 6
The p-value is [tex]p- value = 0.0054[/tex]
Step-by-step explanation:
Considering question 5
Generally the probability of success for a coin toss is [tex]p = 0.5[/tex]
and the probability of failure is [tex]q = 1 - p = 1- 0.5 = 0.5[/tex]
From the question we are told that a certain politician states that the responses are the equivalent of tossing a fair coin.
Also we are told to define success as a participant responding that they support funding, hence
The null hypothesis is [tex]H_o : p = 0.5[/tex]
The alternative hypothesis is [tex]H_A : p \ne 0.5[/tex]
Considering question 6
From the question we are told that
The number that were in favor of the funding is k = 488
The number that were against the funding u = 405
Given that we are to exclude the number that were unsure , then that sample size is mathematically represented as
[tex]n = 488 + 405[/tex]
=> [tex]n = 893[/tex]
Generally the sample proportion of those that are favor of the funding is mathematically represented as
[tex]\^ p = \frac{488}{893 }[/tex]
=> [tex]\^ p = 0.5465[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ p - p }{ \sqrt{\frac{p (1 - p)}{n} } }[/tex]
=> [tex]z = \frac{ 0.5465 - 0.5 }{ \sqrt{\frac{0.5 (1 - 0.5)}{893} } }[/tex]
=> [tex]z = 2.78[/tex]
From the z table
The area under the normal curve to the right corresponding to 2.78 is
[tex]P(Z > 2. 78 ) = 0.0027179[/tex]
Generally the p-value is mathematically represented as
[tex]p- value = 2 * P(Z > 2.78 )[/tex]
=>[tex]p- value = 2 * 0.0027179[/tex]
=>[tex]p- value = 0.0054[/tex]
