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 |
ΣX^{2} |
2238016 |
3027600 |
S^{2}_{X} |
87.88 |
67.17 |
S_{X} |
9.37 |
8.20 |
s^{2}_{X} |
93.73 |
71.37 |
s_{X} |
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?
(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.
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