3a. Machiavelli is interested in how national threats to security affect how citizens view their leaders. He contacts Gallup to obtain information on President Bush's approval ratings one month before the September 11th attacks on the US and one month after the attacks. Gallup provides the data, but warns Machiavelli that (a) those who provided data prior to the attack are not the same people as those who provided data after the attack and (b) only one question was asked to measure approval and participants' responses were limited to approve of Bush's job as president, disapprove, or neither. What statistic shouldMachiavelli use to determine the effect the attacks had on the former president's ratings?

Group of answer choices

Independent samples t-test

Dependent samples t-test

Pearson Correlation

Chi square test of Association

3b. Professor Dumbledore kept records on Hogwarts houses for 30 years. In that time, he found that there was almost always an even distribution of students who were sorted into each house (i.e., 25% were sorted into Gryffindor, Hufflepuff, Ravenclaw and Slytherin).Noting thatthere wasa decrease in Slytherin's popularity after Voldemort tried to take over Hogwarts,Professor McGonagall wants to know if this affected the proportion of new students sorted into Slytherin the following year. What statistical test should she use to determine: Is there a difference in the proportion of students sorted into the houses the year after Voldmort's attack?

Group of answer choices

Independent samples t-test

Spearman Correlation

Chi Square Goodness of Fit

Chi square test of Association