INVESTIGATING STATISTICAL CONCEPTS, APPLICATIONS, AND METHODS

Investigation 1.3.1: Near-Sightedness and Night-Lights

(a) ou = children; variables = eye condition (categorical) and light condition (categorical)

(b) EV = lighting, RV = eye condition

(c) Probably best described cross-classified since both variables were recorded about each child simultaneously. It seems as if the study was retrospective, as researchers relied on memory to record the lighting condition variable.

(d)

(e)

The occurrence of myopia (near-sightedness) appears to increase as the amount of light in the child’s room increases.

(f) .286, .55, .336, .105, .16, .168, .232

About 29% of children were near-sighted, but this proportion increased to .55 for the children with a room light, but was only .105 when no lighting was used.  The occurrence of hyperopia was fairly constant with a slightly increased proportion among children who slept in darkness.

(g) Could be other causes such as genetics, other child-rearing issues that are related to both the type of lighting used and the eye condition of the children.

Investigation 1.3.2: Graduate Admissions Discrimination

(a) men: .445, women: .252

(b) Yes, men were accepted to these Berkeley graduate programs at a much higher rate than women.

(c) program, gender, whether accepted

(d) .619, .059, .824, .070

(e) the issue is that women applied more often to the program that was harder to get into overall.

(f) Since more women applied to program F than program A, the overall acceptance rate for women will be closer to that of program F than that of program A.

(g) (108/449)(.824) + (341/449)(.070) = .25

(h) [825(.619)+373(.059)]/1198 = .44

(i) The two equations will be AmPm + Fm(1-Pm) and AwPm + Fw(1-Pm).  Since Am < Aw and Fm < Fw, the first term is guaranteed to be smaller.

(j) The two equations will be AmPm +Am(1-Pm)  = Am and AwPw + Aw(1-Pw) = Aw.  Since Aw > Am, this will be true about the overall rate as well.