In the 2010 General Social Survey, 17% of Americans said that they had no religious preference. In other words, they said they had “no religion” rather than being Protestant, Catholic, Jewish, or another religion. In 2014, the General Social Survey sampled 2,538 Americans and found that 21% of those surveyed said that they had no religious preference. The resulting p-value is 0.0003; thus, the null hypothesis is rejected. It is concluded that there has been an increase in the proportion of Americans who have no religious preference between 2010 and 2014.What type of error is possible in this situation?Group of answer choicesNeitherBothType IIType I

A 2011 survey by the Bureau of Labor Statistics reported that 91% of Americans have paid leave. In January 2012, a random survey of 1,000 workers showed that 89% had paid leave.The resulting p-value is 0.0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people who have paid leave from 2011 to January 2012.What type of error is possible in this situation?Group of answer choicesNeitherType IBothType II

The decision to reject or fail to reject the null hypothesis is based on:a.The researcher's personal beliefsb.The p-value obtained from the statistical testc.The sample size used in the studyd.The population size used in the study

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

In each of the following examples, a test for the population proportion (p) is called for. You are asked to select the right null and alternative hypotheses.Scenario 1: The UCLA Internet Report (February 2003) estimated that roughly 8.7% of Internet users are extremely concerned about credit card fraud when buying online. Has that figure changed since? To test this, a random sample of 100 Internet users was chosen, and when interviewed, 10 said that they were extremely worried about credit card fraud when buying online. Let p be the proportion of all Internet users who are concerned about credit card fraud.The null hypothesis in this case is:H0: p = 8.7H0: p = 0.087H0: p = 0.10H0: p ≠ 0.087H0: p > 0.087The alternative hypothesis in this case is:Ha: p > 0.087Ha: p < 0.087Ha: p ≠ 0.087Ha: p = 0.087Reset this ActivityScenario 2: The UCLA Internet Report (February 2003) estimated that a proportion of roughly .75 of online homes are still using dial-up access, but claimed that the use of dial-up is declining. Is that really the case? To examine this, a follow-up study was conducted a year later in which out of a random sample of 1,308 households that had Internet access, 804 were connecting using a dial-up modem. Let p be the proportion of all U.S. Internet-using households that have dial-up access.The null hypothesis in this case is:H0: p = 0.75H0: p = 0.615H0: p < 0.75H0: p > 0.615The alternative hypothesis in this case is:Ha: p > 0.75Ha: p < 0.75Ha: p ≠ 0.75Ha: p < 0.615

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.