A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a simple random sample of 500 households in which 200 families agreed. The researchers believe the true proportion of those who agreed would be less than their findings. What is the p-value of their test?

The trustees of a local school district commission a survey to determine voter opinions about a possible bond measure to fund school upgrades. In a poll of 293 of the district’s 5,019 registered voters, 178 would support the bond measure. A hypothesis test was conducted using Minitab to determine if such a bond would pass with the required 55% of the vote.Interpret the meaning of the p-value as a probability statement that relates to this scenario.

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

A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. The p-value is

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. 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%