A sample of 161children was selected from fourth and fifth graders at elementary schools in Philadelphia. In addition to recording 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 contigency table.

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

Step-by-step explanation:

Given that a sample of 161children was selected from fourth and fifth graders at elementary schools in Philadelphia. In addition to recording the grade level, the researchers determined whether each child had a previously undetected reading disability

a) The two qualitative variables are disability and not having disability and secondly the grades of children

b) Contingency table:

Grade 4 5 Total

Normal read. 32 34 66

Not normal read. 23 6 29

Total 55 40 95

H0: Reading disability is independent of grade.

Ha: There is association between the two

c) 4 5 Total

Nor read 38.21052632 27.78947368 66

Not norm 16.78947368 12.21052632 29

Expected cells are obtained using the formula

row total*col total/grand total