Mathematics, 25.12.2019 20:31, lovecats12

What does the result suggest about the politician's claim?

a. the result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss.
b. the result suggests that the politician is correct in claiming that the responses are random guesses equivalent to a coin toss.
c. the results are inconclusive about whether the politician is correct or not.
d. the result suggests that the politician is doing his best to accurately portray the feelings of the people.

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answered: sade20

A. The result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss.

Step-by-step explanation:

Assuming this info: 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 obtained 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 suggest about the politician's claim?

1) Data given and notation

n=882 represent the random sample taken

X=481 represent the adults that were in favor

$\hat p=\frac{481}{882}=0.545$ estimated proportion of adults that were in favor

p_o=0.5 is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that th proportions is equal or not to 0.5:

Null hypothesis: p=0.5

Alternative hypothesis: $p \neq 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.545 -0.5}{\sqrt{\frac{0.5(1-0.5)}{882}}}=2.673$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

p_v =2*P(Z2.673)=0.0075

So the p value obtained was a very low value and using the significance level given $\alpha=0.01$ we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, so the best option is: