I need some help with this exercise for my statistics class. I would appreciate it if anyone could help me, been trying for a while now but I just cant wrap my head around it!
The exercise is:
A student organization plans to ask of 100 randomly selected students whether they favor a change in the grading system. You argue for a sample of 900 students instead of 100. you know that the standard deviation of the proportion p of the sample who say "yes" will be __ times as large with the larger sample. Should this blank be filled with nine, one-ninth, three, or one third?. Explain your answer.
The exercise is:
A student organization plans to ask of 100 randomly selected students whether they favor a change in the grading system. You argue for a sample of 900 students instead of 100. you know that the standard deviation of the proportion p of the sample who say "yes" will be __ times as large with the larger sample. Should this blank be filled with nine, one-ninth, three, or one third?. Explain your answer.
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sample std.dev for proportions is:
sqrt(p(1-p))/(sqrt(n))
y*sqrt(p(1-p))/(sqrt(100)) = sqrt(p(1-p))/(sqrt(900))
y/sqrt(100) = 1/sqrt(900)
y=sqrt(100)/sqrt(900) = 10/30 =1/3
sqrt(p(1-p))/(sqrt(n))
y*sqrt(p(1-p))/(sqrt(100)) = sqrt(p(1-p))/(sqrt(900))
y/sqrt(100) = 1/sqrt(900)
y=sqrt(100)/sqrt(900) = 10/30 =1/3