Some evidence suggests that you are likely to improve your test score if you rethink and change answers on a multiplechoice exam (Johnston. 1975). To examine this phenomenon, a teacher gave the same final exam to two sections of a course. Students in one section were told to turn in their exams immediately after finishing, without changing any answers. In the other section, students were encouraged to reconsider each question and to change answers when they felt it was appropriate. Before the final, the teacher matched 9 students in the first section with 9 students in the second section based on their midterm grades. For example, a student in the nochange section with an 89 cm the midterm was matched with a student in the change section who also had an 89 on the midterm. The final exam grades for the 9 matched pairs of students are presented in the table below.
a. Do the data indicate a significant difference between the two conditions? Use a twotailed test with
b. Construct a 95% confidence interval to estimate the size of the population mean difference.
c. Write a sentence demonstrating how the results of the hypothesis test and the confidence interval would appear in a research report.
a.
Given info:
The given data are shown below,
Matched pair  NoChange Section  Change Section 
#1  71  86 
#2  68  80 
#3  91  88 
#4  65  74 
#5  73  82 
#6  81  89 
#7  85  85 
#8  86  88 
#9  65  76 
Calculation:
The difference D,
Matched pair  NoChange Section  Change Section 


#1  71  86  15  225 
#2  68  80  12  144 
#3  91  88  3  89 
#4  65  74  9  81 
#5  73  82  9  81 
#6  81  89  8  64 
#7  85  85  0  0 
#8  86  88  2  4 
#9  65  76  11  121 
Total 


Thus, the values of
The total number of pairs considered is
The mean difference
Thus, the mean difference
The value of sum of squares,SS is,
Thus, the value of
b.
c.
To write: A sentence demonstrating the way the results of the hypothesis test and confidence interval would appear in a research report.
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