Cardi B is disappointed that the sample from the Bronx, as described in Problem 9, knew on average only 57% of the lyrics of her song “Bodak Yellow.” She says that she can’t declare the Bronx the winner based on what she sees as a low percentage. Instead, she wants to base the contest on the proportion of Bronx residents who got at least 90% of the song’s lyrics right, compared to the residents of the other four boroughs. She says that the Bronx can win the free concert only under two conditions: (1) at least 30% of the Bronx sample got at least 90% of the lyrics right and (2) there is convincing evidence that people in the Bronx are at least 10 percentage points more likely than people from the other four boroughs to know at least 90% of the lyrics of “Bodak Yellow.”

a. Of the Bronx sample, 32% got at least 90% of the lyrics right, compared to 22% of residents from the other boroughs. Does this satisfy Cardi B’s first condition for the Bronx to win the contest?

b. To satisfy the second condition, the Bronx Community College students decide to conduct a one-tailed two-sample hypothesis test at the .05 alpha-
level. Should this be a test for a difference in proportions or means?

c. How many people in total across the two samples got at least 90% of the lyrics of “Bodak Yellow” right? (Refer to Problem 9 for relevant information.)

d. The statistics students find the standard error of the difference to be .07.
Use the standard error to calculate the appropriate test statistic and decide whether to reject the null hypothesis.

e. Should the Bronx win the free concert, according to Cardi B’s second condition?
Explain your answer using the p-value associated with the test statistic from Part d.