Aleyla, an educator, would like to investigate whether students’ IQ have an effect on their exam scores. She also wants to determine if teaching strategy is associated with whether students pass or fail in the exam (exam result). She then randomly selected twenty students and conducted an IQ test. Further, she randomly assigned them to the two teaching strategies. The students’ exam scores were recorded.  1. What can you say about the relationship between IQ and exam scores? Coefficient: __ = ___________   There is a _______ _______ _______ relationship between IQ and exam scores.  2. Test at 5% level of significance if exam scores are linearly associated with IQ. Ho: (in symbols) _____ ; (in words) ____________________________________ Ha: (in symbols) _____ ; (in words) ____________________________________ p-value: ___________ Decision: ________________________________ Conclusion: At alpha = 0.05, ________________________________________________________________ ________________________________________________________________ 3.  Aleyla also wants to know if it is possible to predict the exam scores of students based on IQ. Create a model to do this and interpret its components. Assume all the necessary requirements for a regression analysis were met. Model: ________________________________________ Interpret the following values: Regression constant: ______________________________________________ ________________________________________________________________ Regression coefficient: ?"1 = ______ where ?"1 - coefficient for variable ‘IQ’  The exam scores ________ (increase/decrease) by ________ for every one unit increase in IQ.  R-squared: _________ Interpretation:_____________________________

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Aleyla, an educator, would like to investigate whether students’ IQ have an effect on their exam scores. She also wants to determine if teaching strategy is associated with whether students pass or fail in the exam (exam result). She then randomly selected twenty students and conducted an IQ test. Further, she randomly assigned them to
the two teaching strategies. The students’ exam scores were recorded. 

1. What can you say about the relationship between IQ and exam scores?

Coefficient: __ = ___________  

There is a _______ _______ _______ relationship between IQ and exam scores. 

2. Test at 5% level of significance if exam scores are linearly associated with IQ.

Ho: (in symbols) _____ ; (in words) ____________________________________

Ha: (in symbols) _____ ; (in words) ____________________________________

p-value: ___________

Decision: ________________________________

Conclusion: At alpha = 0.05, ________________________________________________________________ ________________________________________________________________

3.  Aleyla also wants to know if it is possible to predict the exam scores of students based on IQ. Create a model to do this and interpret its components. Assume all the necessary requirements for a regression analysis were met.

Model: ________________________________________

Interpret the following values:

Regression constant: ______________________________________________ ________________________________________________________________

Regression coefficient: ?"1 = ______ where ?"1 - coefficient for variable ‘IQ’ 

The exam scores ________ (increase/decrease) by ________ for every one unit increase in IQ. 

R-squared: _________

Interpretation:_____________________________________________________________________________________________________________________ 

 

 
Doornik-Hansen Test (Exam Scores vs IQ)
DH: 3.808173 p-value:
0.4325889
Correlation Coefficients between Exam Scores and IQ
Pearson's r
Spearman's
Kendall's t=
= 0.7403599
0.6021854
= 0.7680134
Ha: not equal to 0
Ha: not equal to 0
Ha: not equal to 0
p-value = 0.0001894
p-value = 0.0000768
Expected Frequencies of Strategy vs Exam Result
p-value = 0.0002619
strategy F P
128
228
RcmdrMsg: [22] WARNING:
RcmdrMsg- 2 expected frequencies are less than 5
Test of Independence between Strategy and Exam Result
Chi-Square p-
value = 0.2636
Fisher's Exact Test
p-value = 0.582
Regression of Exam Scores on IQ
Coefficients:
(Intercept) -23.9831
0.7955
Estimate Std. Error t value Pr(>|t|)
28.5950 -1.165 0.259419
4.673 0.000189 ***
0.1703
signif. codes:
0.001 *** 0.01
0.05
Residual standard error: 8.92 on 18 degrees of freedom
Multiple R-squared: 0.5481,
F-statistic: 21.83 on 1 and 18 DF, p-value: 0.0001894
Adjusted R-squared: e.523
Transcribed Image Text:Doornik-Hansen Test (Exam Scores vs IQ) DH: 3.808173 p-value: 0.4325889 Correlation Coefficients between Exam Scores and IQ Pearson's r Spearman's Kendall's t= = 0.7403599 0.6021854 = 0.7680134 Ha: not equal to 0 Ha: not equal to 0 Ha: not equal to 0 p-value = 0.0001894 p-value = 0.0000768 Expected Frequencies of Strategy vs Exam Result p-value = 0.0002619 strategy F P 128 228 RcmdrMsg: [22] WARNING: RcmdrMsg- 2 expected frequencies are less than 5 Test of Independence between Strategy and Exam Result Chi-Square p- value = 0.2636 Fisher's Exact Test p-value = 0.582 Regression of Exam Scores on IQ Coefficients: (Intercept) -23.9831 0.7955 Estimate Std. Error t value Pr(>|t|) 28.5950 -1.165 0.259419 4.673 0.000189 *** 0.1703 signif. codes: 0.001 *** 0.01 0.05 Residual standard error: 8.92 on 18 degrees of freedom Multiple R-squared: 0.5481, F-statistic: 21.83 on 1 and 18 DF, p-value: 0.0001894 Adjusted R-squared: e.523
student
strategy ig
score
result
115
78 P
2
103
65 P
110
50 F
4
131
78 P
5
1
132
82 P
6
1
138
95 P
80 P
84 P
E6 P
7
1
115
8
136
9
118
10
104
75 P
80 P
90 P
11
2
126
12
2
141
13
2
130
80 P
14
2
122
55 F
15
2
123
64 P
58 F
65 P
16
2
110
17
112
79 P
62 P
50 F
18
129
19
2
108
20
105
H12 22 222 222 2
123
Transcribed Image Text:student strategy ig score result 115 78 P 2 103 65 P 110 50 F 4 131 78 P 5 1 132 82 P 6 1 138 95 P 80 P 84 P E6 P 7 1 115 8 136 9 118 10 104 75 P 80 P 90 P 11 2 126 12 2 141 13 2 130 80 P 14 2 122 55 F 15 2 123 64 P 58 F 65 P 16 2 110 17 112 79 P 62 P 50 F 18 129 19 2 108 20 105 H12 22 222 222 2 123
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