Polls on certain topics are conducted routinely in order to monitor changes in the public's opinions over time. One such topic is the death penalty. In 2003 a poll estimated that 64% of U.S. adults support the death penalty for a person convicted of murder. In a more recent poll, 675 out of 1,000 U.S. adults chosen at random were in favor of the death penalty for convicted murderers. Do the results of this poll provide evidence that the proportion of U.S. adults who support the death penalty for convicted murderers (p) changed between 2003 and the later poll?State the hypotheses
Question
Polls on certain topics are conducted routinely in order to monitor changes in the public's opinions over time. One such topic is the death penalty. In 2003 a poll estimated that 64% of U.S. adults support the death penalty for a person convicted of murder. In a more recent poll, 675 out of 1,000 U.S. adults chosen at random were in favor of the death penalty for convicted murderers. Do the results of this poll provide evidence that the proportion of U.S. adults who support the death penalty for convicted murderers (p) changed between 2003 and the later poll?State the hypotheses
Solution
The hypotheses for this question would be:
Null Hypothesis (H0): p = 0.64 - This suggests that there is no change in the proportion of U.S. adults who support the death penalty for convicted murderers from 2003 to the later poll.
Alternative Hypothesis (H1): p ≠ 0.64 - This suggests that there is a change in the proportion of U.S. adults who support the death penalty for convicted murderers from 2003 to the later poll.
The next step would be to conduct a hypothesis test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This would involve calculating a test statistic based on the sample data (675 out of 1,000) and comparing it to a critical value. If the test statistic is greater than the critical value, we would reject the null hypothesis and conclude that there is evidence that the proportion of U.S. adults who support the death penalty for convicted murderers has changed. If the test statistic is less than the critical value, we would not reject the null hypothesis and conclude that there is not enough evidence to suggest a change in the proportion.
Similar Questions
Recall the estimate by the Pew Research Center that 62% of U.S. adults favor the death penalty for murder. The same report gave a much lower estimate for the percentage of U.S. college graduates supporting the death penalty in cases of murder. According to census data from 2000, roughly 28% of U.S. adults have a college degree.What is the probability that a randomly selected U.S. adult has a college degree and favors the death penalty?Let A be the event that a U.S. adult has a college degree. Let B be the event that this person supports the death penalty. We want to find P(A and B).Which answer is correct, Answer 1 or 2?Answer 1: P(A and B) = P(A) * P(B) = 0.62(0.28) = 0.1736 We can use the Multiplication Rule for Independent Events because the events are independent. Having a college degree does not determine a person’s views on the death penalty.Answer 2: We do not have enough information to answer the question. We cannot use the Multiplication Rule for Independent Events because these events are dependent. Having a college degree affects the likelihood that a person supports the death penalty.
A Gallup Poll in May 2004 estimated that roughly 70% of U.S. adults are in favor of the death penalty for a person convicted of murder. A random sample of 750 U.S. adults is chosen. Let X be the number of adults (out of 750) who favor the death penalty.The distribution of X is binomial. What are the values of n and p?
Changes in U.S. attitudes toward the death penalty are reflected in the fact that __________.A.there have been no executions in the past five yearsB.the number of executions has been decreasing in recent yearsC.the death penalty is now outlawed in all but five statesD.the annual number of executions has increased steadily since 1990
What kind of poll is used to affect, rather than measure, public opinion?an exit polla push polla random sample polla robo poll
According to GallupLinks to an external site., a public opinion polling organization, which of the following statements is supported by their research?Group of answer choicesPublic confidence in the U.S. Congress has reached an all-time high.A) Voter turnout in the United States has been steadily increasing over the past decade.Americans generally prioritize economic issues over social issues in political decision-making.The majority of Americans trust the federal government to handle domestic issues effectively.Support for same-sex marriage has been consistently declining among Americans.
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