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%

A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.Due to a limited budget, the researcher obtained opinions from a random sample of only 1,432 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)? 0.07% 2.6% 3.0% 5.2%

A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples.If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U.S. adults), what sample size should be used? 17,778 4,445 1,112 67 45

A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people.Which of the following is true regarding the sample proportion p̂ of "yes" responses? The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p. The sample proportion from sample of 100 is more likely to be close to the true population proportion, p. The sample proportion in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.

A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.If the researcher would like to be 95% sure that the obtained sample proportion would be within 2.4% of p (the proportion in the entire population of U.S. adults), what sample size should be used? 6,945 1,737 435 42

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