Studies of children with reading disabilities typically focus on "early-emerging" difficulties identified prior to the fourth grade. Psychologists at Haskins Laboratories recently studied children with

"late-emerging" reading difficulties (i.e., children who appeared to undergo a fourth-grade "slump" in reading achievement) and published their findings in the Journal of Educational Psychology (June 2003). A sample of 161 children was selected from fourth and fifth graders at elementary schools in Philadelphia. In addition to record ing the grade level, the researchers determined whether each child had a previously undetected reading disability.

Sixty-six children were diagnosed with a reading disability.

Of these children, 32 were fourth graders and 34 were fifth graders. Similarly, of the 95 children with normal reading achievement, 55 were fourth graders and 40 were fifth graders.

a. Identify the two qualitative variables (and corresponding levels) measured in the study.

b. From the information provided, form a contingency table.

c. Assuming that the two variables are independent, calculate the expected cell counts.

d. Find the test statistic for determining whether the pro portions of fourth and fifth graders with reading disabilities differs from the proportions of fourth and fifth graders with normal reading skills.

e. Find the rejection region for the test if a = .10.

f. Is there a link between reading disability and grade level? Give the appropriate conclusion of the test.