Ferris Bueller's Day Off

In suburban Chicago, high school senior Ferris Bueller fakes sickness to stay home. Ferris frequently breaks the fourth wall, giving the audience advice on how to skip school, and to narrate about his friends. His younger sister Jeannie is less-convinced, but goes to school anyway. Dean of Students Edward R. Rooney notes and suspects Ferris is being truant again and commits to catching him. However, Ferris uses a computer to alter the school's records to indicate his absences from 9 to 2. Ferris convinces his friend Cameron Frye, who is absent due to illness, to report that his girlfriend Sloane Peterson's grandmother has died. Rooney doubts this, but they succeed as planned.
Borrowing Cameron's father's prized 1961 Ferrari 250 GT California Spyder against Cameron's instinct, Ferris, Cameron, and Sloane drive into Chicago to sightsee. Leaving the car with two parking attendants, who promptly joyride it unknowingly to them, the trio visit the Art Institute of Chicago, Sears Tower, Chicago Mercantile Exchange, and Wrigley Field. They then go to a French restaurant for lunch where Ferris poses as the "Sausage King of Chicago", Abe Froman, while narrowly avoiding his father, who is eating lunch at the restaurant. Meanwhile, after humiliatingly failing to find Ferris, Rooney visits the Bueller residence and fails to enter, being attacked by the family rotweiller as his car is towed. Jeannie, skipping class, returns home and discovers her brother's ruse, but encounters Rooney snooping. She kicks him and calls the police, who arrest her for false reporting after Rooney leaves. While at the station, Jeannie meets a juvenile delinquent, who advises her not to worry so much about Ferris.
After a cab ride where Cameron exclaims disinterest, Ferris impromptu joins a parade float during the Von Steuben Day parade and lip-syncs Wayne Newton's cover of "Danke Schoen", as well as a rendition of The Beatles' "Twist and Shout" that gets the entire crowd dancing. Just as things shine bright, they retrieve the car and notice that, due to the attendants' joyride, over 100 miles have been added. The revelation shocks Cameron into a state of self-analysis, realizing his life is controlled by his father's figure. After coming sane again, they return the car to Cameron's garage and unsuccessfully try to run it backwards to remove the miles; Ferris suggests that they crack it open and turn it back manually. Cameron refuses and vents anger towards his father, kicking, severely denting, and leaning on the car, which falls off the jack and flies out the back, crashing into a ravine behind. Despite Ferris' insistence, Cameron decides to take a stand against his father after destroying the car. At the police station, Mrs. Bueller picks up Jeannie, whom she finds kissing the delinquent.
Ferris returns Sloane home, but realizes he only has a limited time to return home to avoid trouble. He rushes back to the house, but is spotted by Jeannie driving their mother home, and tries to run him down. Ferris avoids being noticed by Mrs. and Mr. Bueller, who is coming from another direction. They make it home at the same time, but Rooney catches Ferris trying to enter the back door and rhetorically asks if he would like to spend another year under supervision. However, Jeannie discovers his wallet on the kitchen floor as proof he broke in, and she has a change of heart, letting Ferris in and telling Rooney he was hospitalized â indicating awareness of the break-in. She slams the door, and their dog attacks Rooney again. Ferris leaps into his bed at the last second, assuring his parents don't suspect a thing. As they leave, Ferris reminds the audience, "Life moves pretty fast. If you don't stop and look around once in a while, you could miss it." Ferris then smiles at the camera before fading to black.
As the credits roll, the defeated Rooney heads home and is picked up by a school bus, further humiliated by the students, one offering him a gummy bear. In a post-credits scene, Ferris emerges from his room and bids everyone that "It's over," and to go home.

Question: Which of Sloane's family members does Ferris pretend has died?
Answer: grandmother