Resolviendo el reto

Mi test, haciendo la llamada desde el debug element y comprobando el selectedPerson de acuerdo al índice seleccionado del array de people.

it('should raise selected event when clicked', () => {
    // Arrange
    component.people = [
      new Person('Leonardo', 'Arias', 23, 1, 1),
      new Person('Valentina', 'Rodriguez', 12, 2, 3),
      new Person('Santiago', 'Dolores', 12, 2, 3),
    ];
    const idx = 1;
    //Act
    fixture.detectChanges();
    const debugElement = fixture.debugElement.queryAll(By.css('app-person'));
    const btnDe = debugElement[idx].query(By.css('.btn-choose'));
    btnDe.triggerEventHandler('click', null);
    fixture.detectChanges();
    //
    expect(component.selectedPerson).toEqual(component.people[idx]);
  });

Yo realice un test probando validando los 2 casos en una

it('sould render selected person after choose person', () => {
    // Arrange
    component.people = [
      new Person('Jorge', 'Medina', 25, 67.2, 1.81),
      new Person('Glenda', 'López', 24, 62, 1.75),
      new Person('Mariana', 'López', 5, 30, 1.4),
    ];
    const personName = component.people[0].name;
    // Act
    fixture.detectChanges();
    const personDebug = fixture.debugElement.query(By.css('app-person'));
    const btnDebug = personDebug.query(By.css('.btn-choose'));
    btnDebug.triggerEventHandler('click', null);
    fixture.detectChanges();
    const liNameEl: HTMLElement = fixture.debugElement.query(
      By.css('div ul li')
    ).nativeElement;
    // Assert
    expect(component.selectedPerson).toEqual(component.people[0]);
    expect(liNameEl?.textContent).toContain(component.people[0].name);
  });

Yo hice el test de una manera diferente cuando es llamada la función choose y llena la variable selectedPerson.

   it('Should fill selectedPerson when choose function has been called', () => {
      component.selectedPerson = new Person('', '', 0, 0, 0);
      component.people = [
        new Person('Miguel', 'Coy', 30, 72, 1.76),
        new Person('Ernesto', 'Pérez', 30, 60, 1.8),
      ];
      component.choose(component.people[0]);
      fixture.detectChanges();
      expect(component.selectedPerson).toEqual(component.people[0]);
      component.choose(component.people[1]);
      fixture.detectChanges();
      expect(component.selectedPerson).toEqual(component.people[1]);
    });