Practice Exercise 24: Determining the Appropriate Analysis For each of the follo
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Practice Exercise 24: Determining the Appropriate Analysis
For each of the following scenarios, identify the appropriate analysis.
1. The question is whether verbal reinforcement affects response rates. Subjects in Group 1 were verbally reinforced every time they respond to the instructor’s questions. Subjects in Group 2 were not. After 2 weeks, the two groups were compared by gauging the number of students who raised their hand when questions were asked. The following data were collected.
Group 1: 13, 15, 12, 17, 14, 14,
Group 2: 10, 12, 12, 11, 13, 9
2. Assume that an educator wants to know how closely time spent doing homework is related to student grades. Data was collected from 8 students. Time spent on homework is reported in the number of hours completed per night, and grades are reported on a 4-point scale. The following data were collected.
3. Three groups of students involved in the same curriculum are obliged to study for 15 minutes, 30 minutes, or 90 minutes a night for 8 weeks before taking a mathematics test. Scores from 5 students in each group were randomly selected to determine if there was a difference among the three time groups. Their scores are as follows:
15 minutes: 43, 39, 55, 56, 73
30 minutes: 55, 58, 66, 79, 82
90 minutes: 61, 66, 85, 86, 91
4. An administrator is interested in determining if the type of reading curriculum students receive is related to whether they meet reading standards for their grade. The following data were collected.
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Student Homework Grades 1 .25 2.00 2 .50 1.75 3 .75 2.00 4 1.00 2.50 5 1.00 2.00 6 1.25 2.25 7 1.50 2.00 8 2.00 3.60Explanation / Answer
Q 1. Ans: Two sample t-test.
Two-Sample T-Test and CI: Group 1, Group 2
Two-sample T for Group 1 vs Group 2
N Mean StDev SE Mean
Group 1 6 14.17 1.72 0.70
Group 2 6 11.17 1.47 0.60
Difference = mu (Group 1) - mu (Group 2)
Estimate for difference: 3.000
95% CI for difference: (0.908, 5.092)
T-Test of difference = 0 (vs not =): T-Value = 3.24 P-Value = 0.010 DF = 9
The estimated p-value is 0.01. hence, we can not accept the null hypothesis and conclude that there is significant affects of verbal reinforcement response rates at o.05 level of significance.
Q 2. Ans: The analysis will do by simple regression analysis
Regression Analysis: Grades versus Homework
The regression equation is
Grades = 1.45 + 0.790 Homework
Predictor Coef SE Coef T P
Constant 1.4478 0.3233 4.48 0.004
Homework 0.7900 0.2798 2.82 0.030
S = 0.413023 R-Sq = 57.1% R-Sq(adj) = 49.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 1.3602 1.3602 7.97 0.030
Residual Error 6 1.0235 0.1706
Total 7 2.3837
The estimated p-value of Homework coefficient is 0.030. Hence, we can not accept the null hypothesis and conclude that homework has a significant association with the grade of the student at 0.05 level of significance.
Q 3. Ans: One-way Analysis of variance that is One way ANOVA test will apply to this question.
One-way ANOVA: Y versus Time
Source DF SS MS F P
Time 2 1534 767 4.57 0.033
Error 12 2014 168
Total 14 3547
S = 12.95 R-Sq = 43.24% R-Sq(adj) = 33.78%
Conclusion: The estimated p-value is 0.033. Hence we can conclude that at least two-time groups have different mathematics score at 0.05 level of significance.
Q 4 Ans: This question will solve by Chi-square test for independence.
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