A certain college claims that 58% of its incoming students will graduate with a

Question

A certain college claims that 58% of its incoming students will graduate with a degree or certificate. You think this estimate is much too high so you decide to do your own study.  

A.) Assuming the normal model applies, what is the mean (expected Value) for the sampling distribution of the proportion of students who graduate with a degree or certificate from this college?

B.) Based on a random sample of 120 former students you find that only 61 of them actually graduated with a degree or certificate. Find the standard deviation for the sampling distribution of the proprtion of students who graduate with a degree or certificate from this college.  

C.) Using your parameters from p parts a and b, determine if your sample results are unusual compared to the colleges claim. Justify your answer with statistical evidence.

Explanation / Answer

Ans:

sampling distribution of sample proportions:

mean=p

standard deviation=sqrt(p*(1-p)/n)

a)mean=0.58

b)standard deviation=sqrt(0.58*(1-0.58)/120)=0.045

c)sample proportion=61/120=0.5083

z=(0.5083-0.58)/0.045

z=-1.59

As,z=-1.59 lies between z=-2 and z=2,so not unusual.

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