In Arizona, all students in elementary and secondary schools have to take AIMS t
ID: 3368722 • Letter: I
Question
In Arizona, all students in elementary and secondary schools have to take AIMS tests (which was largely replaced by AZmerit tests recently) as the state-mandated standardized assessment of math and English proficiency. A teacher wonders if high school dropout rate would be correlated with AIMS test results in a particular county. To explore this question, she collected the dropout rates and the AIMS Math pass rates (taken in 2012) at the county level for cohort 2014 from all counties in Arizona, as listed in the table below.
County ID #
AIMS Math Pass Rate (%)
Dropout Rate (%)
1-Apache
39
33
2-Cochise
55
20
3-Coconino
60
24
4-Gila
40
25
5-Graham
56
22
6-Greenlee
54
14
7-La Paz
48
30
8-Maricopa
64
23
9-Mohave
52
25
10-Navajo
49
21
11-Pima
55
29
12-Pinal
53
29
13-Santa Cruz
57
15
14-Yavapai
61
21
15-Yuma
45
23
Calculate the Z scores for all the scores of AIMS English pass rate and high school dropout rate, separately. (please show work for a few so I understand how to do it)
Explain the direction and strength of the relationship based on the r.
County ID #
AIMS Math Pass Rate (%)
Dropout Rate (%)
1-Apache
39
33
2-Cochise
55
20
3-Coconino
60
24
4-Gila
40
25
5-Graham
56
22
6-Greenlee
54
14
7-La Paz
48
30
8-Maricopa
64
23
9-Mohave
52
25
10-Navajo
49
21
11-Pima
55
29
12-Pinal
53
29
13-Santa Cruz
57
15
14-Yavapai
61
21
15-Yuma
45
23
Explanation / Answer
Sol"
Zscore=X-mean/stddev
For Ex
For AIMS math rate of 39
Z=39-52.5333/7.249
Z=-1.866
r=-0.445
There exists a moderate negative relatinship between AIIMS Math pass rate and drop out rate.
Form linear
Direction :negative
Strength:moderate
County ID # AIMS Math Pass Rate (%) AIMS mean AIMS stddev Z score AIIMS Dropout Rate (%) Drop out Rate Mean Drop out Rate stddev Z score Drop out 1-Apache 39 52.53333333 7.249302101 -1.866846372 33 23.6 5.261721609 1.786487522 2-Cochise 55 52.53333333 7.249302101 0.34026264 20 23.6 5.261721609 -0.684186711 3-Coconino 60 52.53333333 7.249302101 1.029984206 24 23.6 5.261721609 0.076020746 4-Gila 40 52.53333333 7.249302101 -1.728902059 25 23.6 5.261721609 0.26607261 5-Graham 56 52.53333333 7.249302101 0.478206953 22 23.6 5.261721609 -0.304082983 6-Greenlee 54 52.53333333 7.249302101 0.202318327 14 23.6 5.261721609 -1.824497895 7-La Paz 48 52.53333333 7.249302101 -0.625347553 30 23.6 5.261721609 1.21633193 8-Maricopa 64 52.53333333 7.249302101 1.581761459 23 23.6 5.261721609 -0.114031118 9-Mohave 52 52.53333333 7.249302101 -0.0735703 25 23.6 5.261721609 0.26607261 10-Navajo 49 52.53333333 7.249302101 -0.48740324 21 23.6 5.261721609 -0.494134847 11-Pima 55 52.53333333 7.249302101 0.34026264 29 23.6 5.261721609 1.026280066 12-Pinal 53 52.53333333 7.249302101 0.064374013 29 23.6 5.261721609 1.026280066 13-Santa Cruz 57 52.53333333 7.249302101 0.616151266 15 23.6 5.261721609 -1.634446031 14-Yavapai 61 52.53333333 7.249302101 1.167928519 21 23.6 5.261721609 -0.494134847 15-Yuma 45 52.53333333 7.249302101 -1.039180493 23 23.6 5.261721609 -0.114031118