In May 2012, President Obama made history by revealing his support of gay marriage. Around that time, the Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbian relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable" and that 50% felt that gay marriage should be legal.
1. Does this sample provide evidence that the majority of Americans find gay/lesbian relations "morally acceptable"? Describe how you could generate a single randomization sample in this situation, and identify the statistic that you would calculate for each sample.
2. Use technology to determine if this sample provides evidence that the majority of Americans find gay/lesbian relations "morally acceptable". Be sure to state the hypotheses, give the p-value, and clearly state the conclusion in context. Include an assessment of the strength of the evidence.
3. Use the provided randomization distribution (based on 1,000 samples) to determine if this sample provides evidence that the majority of Americans find gay/lesbian relations "morally acceptable". Be sure to state the hypotheses, give the p-value, and clearly state the conclusion in context. Include an assessment of the strength of the evidence.
4. Define the appropriate parameter and state the hypotheses for testing if this sample provides evidence that the proportion of American adults who support gay marriage differs from 50%.
5. A 90% confidence interval for the proportion of American adults who support gay marriage is (0.475, 0.524). Does this confidence interval provide evidence that the percentage of American adults who support gay marriage differs from 50%? Briefly justify your answer and state the significance level you are using.