In 2010, 65% of adult Americans thought that the death penalty was morally acceptable. In a poll conducted by the Gallup Organization, a simple random sample of 1005 adult Americans resulted in 704 respondents stating that they believe the death penalty was morally acceptable when asked, "Do you believe the death penalty is morally acceptable or morally wrong?" (The choices, "morally acceptable" and "morally wrong" were randomly interchanged in the question for each interview.) Is there significant evidence at the 5% level of significance to indicate that the proportion of adult Americans who believe the death penalty is morally acceptable, has increased from the level reported in 2010?
p = 65% = 0.65
p_bar = (704/1005) = 0.70
Standard error = sqrt( p_bar * (1-p_bar)/n )= sqrt(0.70 * (1-0.70) / 1005) = 0.0145
Here a statistical test is carried out to test whether proportion of Americans has increased who think death penalty is morally accepted.