In order to understand more about how people in the U.S. feel about the outcome
ID: 3272916 • Letter: I
Question
In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the 562 people who voted in the poll indicated they were unhappy with the verdict. Evaluate the strength of evidence for the hypothesis that the proportion of U.S. adults opposed to the verdict is greater than 0.75.
1)Find the p-value for the hypothesis using a simulation-based approach. Based on the p-value evaluate the strength of evidence and state a conclusion about the opinions of U.S. adults about the verdict.
There is evidence that the proportion of U.S. adults opposed to the verdict is less than 75%.
There is weak evidence that the proportion of U.S. adults opposed to the verdict is greater than 75%.
There is strong evidence that the proportion of U.S. adults opposed to the verdict is greater than 75%.
There is no evidence that the proportion of U.S. adults opposed to the verdict is greater than 75%.
2) To which population, if any, are you comfortable drawing your conclusion?
Comfortable in generalizing to all adults in the U.S.
Comfortable in generalizing to all people who watch this program and are motivated to participate.
Comfortable in generalizing to all people who might watch this program.
3) Explain why a theory-based approach is or is not reasonable for these data. If a theory-based approach is reasonable, find the p-value.
Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0001.
Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0002.
Theory-based is not appropriate because there are not enough data values.
Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.1.
Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0001.
Explanation / Answer
1. H0 : p <= 0.75
Ha : p > 0.75
where p is the proportion of people who were unhappy with the verdict.
By simulation based approach, There is strong evidence that the proportion of U.S. adults opposed to the verdict is greater than 75%.Opion C is correct.
2. We are comfortable with in generalizing to all people who watch this program and are motivated to participate.
3. Theory based approach is correct
Test statistic :
Z = (p - p0)/ sqrt [p0 (1-p0)/N]
Z = (0.82 - 0.75)/ sqrt (0.75 * 0.25/ 562)
Z = 0.07/ 0.0186 = 3.83
p = 0.0001
Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0001.
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