A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test
this claim, he selects random cities in the state that voted the senator in and compares the approval ratings before the decision to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after the decision. Assume that the percentages are normally distributed. What type of test is this hypothesis test?
A paired sample t-test is most of the time used when in determining the difference between two related dependent variables and in this context; we have
approval ratings before the senator's decision variables and
approval rating after the senator's decision variables for the same subject
These revolves around the senator's decision causing a decrease in approval ratings. Often the two variables are separated by time.
It is used to determine whether the mean of the dependent variable (approval ratings) is the same in the two related groups (the before and after decision groups).
