FCAT scores and poverty. Refer to the Journal of Educational and Behavioral Statistics (Spring 2004) study of scores on the Florida Comprehensive Assessment Test (FCAT), first presented in Exercise.
FCAT scores and poverty. In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam, called the Florida Comprehensive Assessment Test (FCAT). An analysis of the link between FCAT scores and sociodemographic factors was published in the Journal of Educational
Elementary School | FCAT—Math | FCAT—Reading | % Below Poverty |
1 | 166.4 | 165.0 | 91.7 |
2 | 159.6 | 157.2 | 90.2 |
3 | 159.1 | 164.4 | 86.0 |
4 | 155.5 | 162.4 | 83.9 |
5 | 164.3 | 162.5 | 80.4 |
6 | 169.8 | 164.9 | 76.5 |
7 | 155.7 | 162.0 | 76.0 |
8 | 165.2 | 165.0 | 75.8 |
9 | 175.4 | 173.7 | 75.6 |
10 | 178.1 | 171.0 | 75.0 |
11 | 167.1 | 169.4 | 74.7 |
12 | 177.0 | 172.9 | 63.2 |
13 | 174.2 | 172.7 | 52.9 |
14 | 175.6 | 174.9 | 48.5 |
15 | 170.8 | 174.8 | 39.1 |
16 | 175.1 | 170.1 | 38.4 |
17 | 182.8 | 181.4 | 34.3 |
18 | 180.3 | 180.6 | 30.3 |
19 | 178.8 | 178.0 | 30.3 |
20 | 181.4 | 175.9 | 29.6 |
21 | 182.8 | 181.6 | 26.5 |
22 | 186.1 | 183.8 | 13.8 |
Based on Tekwe, C. D., et al. “An empirical comparison of statistical models for value-added assessment of school performance.” Journal of Educational and Behavioral Statistics , Vol. 29, No. 1, Spring 2004.
and Behavioral Statistics (Spring 2004). Data on average math and reading FCAT scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 Florida elementary schools are listed in the accompanying table and saved in the FCAT file.
a. Propose a straight-line model relating math score ( y ) to percentage ( x ) of students below the poverty level.
b. Use the method of least squares to fit the model to the data in the FCAT file.
c. Graph the least squares line on a scatterplot of the data. Is there visual evidence of a relationship between the two variables? Is the relationship positive or negative?
d. Interpret the estimates of the y -intercept and slope in the words of the problem.
e. Now consider a model relating reading score ( y ) to percentage ( x ) of students below the poverty level. Repeat parts a–d for this model.
Consider the simple linear regression relating math score ( y ) to percentage ( x ) of students below the poverty level. The data are saved in the FCAT file.
a. Test whether y is negatively related to x. Use α = .01
b. Construct a 99% confidence interval for β1. Interpret the result practically.
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