The following binary data represent the students taking a statistics course in a major university, where "1" is for students who are business majors and "0" for other majors. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1   27 If we take repeated samples of size n = 8 from this population of the students, the expected value of sample proportions would be ______.   a 0.895                 b 0.865                 c 0.836                 d 0.808

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The following binary data represent the students taking a statistics course in a major university, where "1" is for students who are business majors and "0" for other majors.
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 0 1 1 1
1 1 1 1 1 0 1 1 1 1
1 0 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 0 1 0 0 1 1 1 1 1
1 1 1 1 1 1 1 1 0 1
0 1 0 1 1 1 1 1 1 1
1 1 1 1 1 0 1 1 1 0
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 0 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 0 1 1 1 1 1 1 0 1
1 1 1 1 1 1 1 1 1 0
1 1 1 1 1 1 1 0 1 1
1 0 1 0 0 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1
1 1 1 0 1 1 1 0 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
0 1 1 1 1 1 1 0 1 1
1 1 0 0 0 0 1 1 1 1
1 1 1 1 0 0 1 1 1 0
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 0 1 1 0 1
1 1 1 1 1 0 1 1 1 1
1 0 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 0 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 0 1 1 1 1
1 1 1 0 0 1 1 1 1 1
1 1 1 1 1 1 1 0 1 1
1 1 1 1 1 0 1 1 1 1
1 0 0 0 1 0 1 1 1 0
1 1 1 0 1 1 1 1 0 1
1 1 1 0 1 1 0 1 1 1
1 1 1 1 0 1 1 1 1 1
1 1 1 1 1 1 1 0 1 1
1 1 1 1 1 1 1 1 0 1

 

27 If we take repeated samples of size n = 8 from this population of the students, the expected value of sample proportions would be ______.
 
a 0.895                
b 0.865                
c 0.836                
d 0.808                
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