Q1) A local school board wanted to compare test scores on standardized mathematics tests for 9th grade students in 2 different junior high schools. A random sample of 10 students from school A and a random sample of 10 students from school B were selected and scores were recorded as shown:
|
School A
|
School B
|
|
631
|
642
|
|
566
|
710
|
|
620
|
649
|
|
542
|
596
|
|
560
|
660
|
|
669
|
722
|
|
644
|
769
|
|
600
|
723
|
|
610
|
649
|
|
559
|
766
|
a) Identify the type of experimental design used and identify all independent and dependent variables.
b) Conduct the correct test of hypothesis.
c) Provide the appropriate hypotheses for this design. Test all hypotheses at alpha =0.05. Do the data indicate a significant difference in scores between the 2 schools?
d) If there are differences, please indicate where they are.
Q2) The Academic Performance Index (API) measures achievement based on the Stanford 9 Achievement Test. Scores go from 200 to 21000 with 800 as the long-range goal for all students. Eight elementary schools in a certain county along with the percent of students at that school considered English Language Learners is provided.
|
School
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
API
|
588
|
659
|
710
|
657
|
669
|
641
|
557
|
743
|
|
ELL
|
58
|
22
|
14
|
30
|
11
|
26
|
39
|
6
|
a) Identify the independent and dependent variables.
b) Plot the data. Is the assumption of linear relationship justified?
c) If so, find the linear regression line. State and test the hypotheses of correlation and linear regression. State and test all assumptions.
Q3) Consider the same API index. Suppose you wish to determine the relationship between the API score and 4 independent variables as displayed below:
|
School
|
Y
|
x1
|
x2
|
x3
|
x4
|
x5
|
|
1
|
588
|
yes
|
58
|
34
|
16
|
533
|
|
2
|
659
|
no
|
62
|
22
|
5
|
655
|
|
3
|
710
|
yes
|
66
|
14
|
19
|
695
|
|
4
|
657
|
no
|
36
|
30
|
14
|
680
|
|
5
|
669
|
no
|
40
|
11
|
13
|
670
|
|
6
|
641
|
no
|
51
|
26
|
2
|
636
|
|
7
|
557
|
no
|
73
|
39
|
14
|
532
|
|
8
|
743
|
yes
|
22
|
6
|
4
|
705
|
The variables are defined as:
X1 = 1 if the school was given financial award for meeting growth goals, 0 if not.
X2 = % of students who qualify for free or reduced price meals.
X3 = % of students who are English Language Learners.
X4 = % of teachers on emergency credentials
X5 = previous API score.
a) Identify the experimental design used. Identify all independent and dependent variables. Find the least-square prediction equation.
b) Discuss how well the data fits the data using the correlation coefficient.
c) Which if any of the independent variables are useful in predicting the API given the other independent variables already in the model? Explain using the beta coefficients of the regression model.
d) Choose the best model using R2 and R2 (adj). Identify all hypotheses.
Q4) Identify a specific situation where you as a researcher would or could use this data for a multiple regression. Address all assumptions including multi-collinearity. Identify all variables. Set up the correct hypotheses and provide clear and correct interpretations.
|
N
|
y
|
x1
|
x2
|
x3
|
x4
|
|
1
|
69
|
6
|
1
|
2
|
1
|
|
2
|
118.5
|
10
|
1
|
2
|
2
|
|
3
|
116.5
|
10
|
1
|
3
|
2
|
|
4
|
125
|
11
|
1
|
3
|
2
|
|
5
|
129.9
|
13
|
1
|
3
|
1.7
|
|
6
|
135
|
13
|
2
|
3
|
2.5
|
|
7
|
139.9
|
13
|
1
|
3
|
1
|
|
8
|
147.9
|
17
|
2
|
3
|
2.5
|
|
9
|
160
|
19
|
2
|
3
|
2
|
|
10
|
169.9
|
18
|
1
|
3
|
2
|
|
11
|
134.9
|
13
|
1
|
4
|
2
|
|
12
|
155
|
18
|
1
|
4
|
2
|
|
13
|
169.9
|
17
|
2
|
4
|
3
|
|
14
|
194.5
|
20
|
2
|
4
|
3
|
|
15
|
209.9
|
21
|
2
|
4
|
3
|