Question

In: Statistics and Probability

In Arizona, all students in elementary and secondary schools have to take AIMS tests (which was...

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.

Solutions

Expert Solution

Sol"

Zscore=X-mean/stddev

For Ex

For AIMS math rate of 39

Z=39-52.5333/7.249

Z=-1.866

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
AIMS Math Pass Rate (%) Dropout Rate (%)
AIMS Math Pass Rate (%) 1
Dropout Rate (%) -0.44531 1

r=-0.445

There exists a moderate negative relatinship between AIIMS Math pass rate and drop out rate.

Form linear

Direction :negative

Strength:moderate

orchestra answered 2 years ago
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