Students who graduated from college in last year with student loans owed an average of $25,250 (The New York Times, November 2). An economist wants to determine if the average debt has increased since last year. She takes a sample of 40 recent graduates and finds that their average debt was $28,275. Assume that the population standard deviation is $7,250. a. Specify the competing hypotheses to determine whether the average undergraduate debt has increased since last year. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, can you conclude that the average undergraduate debt has increased?

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .