Learn By DoingThe following two hypotheses are tested:Ho: The proportion of U.S. adults who oppose gay marriage is roughly 50%.Ha: The proportion of U.S. adults who oppose gay marriage is above 50% (i.e., the majority oppose).Suppose a survey was conducted in which a random sample of 1,100 U.S. adults was asked about their opinions about gay marriage, and based on the data, the p-value was found to be .002.Comment: Throughout this activity use a .05 (5%) significance level (cutoff).The fact that the p-value = .002 means that:There is .002 probability of observing data like those observed.There is .002 probability that 50% of U.S. adults oppose gay marriage.There is a probability of .002 (i.e., very unlikely) to observe data like those observed if the proportion of U.S. adults who oppose gay marriage were 50%.There is .998 probability that the majority of U.S. adults oppose gay marriage.Reset this ActivityBased on the p-value you can conclude that:the data provide significant evidence that the proportion of U.S. adults who oppose gay marriage is 50%.the data provide significant evidence that the majority of U.S. adults oppose gay marriage.the data do not provide enough evidence to conclude that the majority of U.S. adults oppose gay marriage.the data provide evidence that Ha is more likely than Ho (i.e., it is more likely that the majority of U.S. adults oppose gay marriage).Reset this ActivitySay that the p-value was not given, but rather, the following conclusion was advertised: "The survey does not provide enough evidence to conclude that the majority of U.S. adults oppose gay marriage." Which of the following could have been the p-value that led to this conclusion?.1251.96.045-1.96Reset this ActivityWhen would you conclude that the data provide enough evidence that the proportion of U.S. adults who oppose gay marriage is 50%?when the p-value is small (less than .05)when the p-value is not small (above .05)when exactly half the individuals in the sample oppose gay marriage and half support itnever
Question
Learn By DoingThe following two hypotheses are tested:Ho: The proportion of U.S. adults who oppose gay marriage is roughly 50%.Ha: The proportion of U.S. adults who oppose gay marriage is above 50% (i.e., the majority oppose).Suppose a survey was conducted in which a random sample of 1,100 U.S. adults was asked about their opinions about gay marriage, and based on the data, the p-value was found to be .002.Comment: Throughout this activity use a .05 (5%) significance level (cutoff).The fact that the p-value = .002 means that:There is .002 probability of observing data like those observed.There is .002 probability that 50% of U.S. adults oppose gay marriage.There is a probability of .002 (i.e., very unlikely) to observe data like those observed if the proportion of U.S. adults who oppose gay marriage were 50%.There is .998 probability that the majority of U.S. adults oppose gay marriage.Reset this ActivityBased on the p-value you can conclude that:the data provide significant evidence that the proportion of U.S. adults who oppose gay marriage is 50%.the data provide significant evidence that the majority of U.S. adults oppose gay marriage.the data do not provide enough evidence to conclude that the majority of U.S. adults oppose gay marriage.the data provide evidence that Ha is more likely than Ho (i.e., it is more likely that the majority of U.S. adults oppose gay marriage).Reset this ActivitySay that the p-value was not given, but rather, the following conclusion was advertised: "The survey does not provide enough evidence to conclude that the majority of U.S. adults oppose gay marriage." Which of the following could have been the p-value that led to this conclusion?.1251.96.045-1.96Reset this ActivityWhen would you conclude that the data provide enough evidence that the proportion of U.S. adults who oppose gay marriage is 50%?when the p-value is small (less than .05)when the p-value is not small (above .05)when exactly half the individuals in the sample oppose gay marriage and half support itnever
Solution
The text you provided is a series of questions related to hypothesis testing in statistics, specifically about the proportion of U.S. adults who oppose gay marriage. Here are the answers:
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The fact that the p-value = .002 means that there is a probability of .002 (i.e., very unlikely) to observe data like those observed if the proportion of U.S. adults who oppose gay marriage were 50%.
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Based on the p-value you can conclude that the data provide significant evidence that the majority of U.S. adults oppose gay marriage.
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If the conclusion was "The survey does not provide enough evidence to conclude that the majority of U.S. adults oppose gay marriage," the p-value that could have led to this conclusion could be .125.
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You would conclude that the data provide enough evidence that the proportion of U.S. adults who oppose gay marriage is 50% when the p-value is not small (above .05).
Similar Questions
A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples. Due to a limited budget, the researcher obtained opinions from a random sample of only 2,222 U.S. adults.With this sample size, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than which of the following percentages (answers are rounded)?Group of answer choices2.1%0.75%3%0.04%
Suppose that a major polling organization wanted to test the hypothesis that there was a change in the president’s “approval rating” since last month. Last month, 35% of the representative sample of registered voters approved of the president. For this month, the null hypothesis was that the approval rating equals 35% and the alternative hypothesis is that the approval rating does not equal 35%. The significance level for this test was 0.05.The results of the hypothesis test of the new survey showed a p-value of 0.008.Which of the following statements is correct? Check all that apply. The results were statistically significant. The results were not statistically significant. The null hypothesis should be rejected. The null hypothesis should be accepted. The null hypothesis cannot be rejected.
Based on the p-value, what is your conclusion (use .05 significance level)?
Your study is only valid if your p-value is < 0.05.Group of answer choicesTrueFalse
Which of the following facts about the p-value of a test is correct? The larger the p-value, the more evidence the data provide against H0. Regardless of the significance level, a p-value of 0.01 provides enough evidence to reject H0. A p-value smaller than the significance level provides enough evidence to reject H0.
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