Question

An Illinois state program evaluator is tasked with studying the intelligence of soon graduating high school students in a number of Chicago-area high schools.

One of the specific questions that needs to be answered is, “How do the students of Collins High School, one of Chicago’s lowest-rated high schools in terms of academic achievement, fare compared to students of Lincoln Park High School, one of Chicago’s highest-rated high schools in terms of academic achievement?”.

To conduct this study, the program evaluator administers the Wechsler Adult Intelligence Scale, 4th Edition (WAIS-IV) to one 12th grade class from each high school in the Chicago area (if you are interested in learning more about the WAIS-IV, click here).

The following table shows the WAIS-IV scores for student from Collins HS and Lincoln Park HS (note: data were fabricated for purposes of this exercise):

Collins HS		Lincoln Park HS
Student	WAIS-IV Score	Student	WAIS-IV Score
1	105	1	93
2	81	2	90
3	102	3	87
4	90	4	109
5	95	5	106
6	110	6	104
7	90	7	109
8	100	8	104
9	80	9	115
10	90	10	112
11	84	11	112
12	81	12	100
13	90	13	97
14	107	14	90
15	101	15	104
16	90	16	107
		17	101

Also, here is the frequency table showing the frequency of grouped WAIS-IV scores for each HS:

WAIS-IV Score	Collins HS ( f )	Lincoln Park HS ( f )
80-89	4	1
90-99	6	4
100-109	5	9
110-119	1	3

And the correct answers to the table of important computations:

MEASURE	Collins HS ( f )	Lincoln Park HS ( f )
Mean	93.50	102.35
Median	90	104
Mode	90	104
N	16	17
N-1	15	16
ΣX	1496	1740
(ΣX)2	141282	179236
ΣX2	2238016	3027600
S2X	87.88	67.17
SX	9.37	8.20
s2X	93.73	71.37
sX	9.68	8.45

Use the above information to answer the following questions (round to two decimal places where necessary):

1. What is the z-score of student 12 from Collins HS?

2. What is the raw WAIS-IV score of the student from Lincoln Park HS with a z-score of +0.61?

3. What is the z-score for student 11 at Lincoln HS? Would their z-score increase or decrease if they went to Collins HS? By how much?

4. Which student has a better WAIS-IV score relative to his/her respective peers (i.e., students from their HS): student 8 from Collins HS or student 7 from Lincoln Park HS? Why?

Answer 1

(1) z-score = (81 - 93.50)/9.68 = -1.29

(2) raw score = (0.61 * 9.68) + 93.50 = 99.41

(3) z-score of student 11 at Lincoln HS = (112 - 102.35)/8.45 = 1.14
If he/she moved to Collins HS, then z-score would be = (112 - 93.50)/9.68 = 1.91
Z-score would have increased by 0.77

(4) z-score of student 8 from Collins HS = (100 - 93.50)/9.68 = 0.67
z-score of student 7 from Lincoln Park HS = (109 - 102.35)/8.45 = 0.79
Since the z-score of student 7 is higher, we can say that he/she has a better WAIS-IV score than student 8 of Collins HS.