According to the Institute for College Access and Success, 69% of students who g

Question

According to the Institute for College Access and Success, 69% of students who graduated from college in 2013 had student loan debt. You want to know if the proportion is the same in Wisconsin as in the US as a whole, so you survey a random sample of 100 people who graduated from Wisconsin colleges in 2013. You find that 76 of them had student loan debt. a. Assuming that the proportion of people with student loan debt is the same in Wisconsin as in the whole US, what is the probability that 76 or more people in your sample have student loan debt? Use a normal approximation for p^p^.

Explanation / Answer

Given, p = 0.69, n = 100

For normal approximation, np>=5 and n(1-p)>=5 must be satisfied.

100*0.69 = 69 and 100*0.31 = 31, Hence we can approximate the sampling distribution to normal.

standard deviation, s = sqrt(p*(1-p)/n) = sqrt(0.69*0.31/100) = 0.0462493

For probability of 76 or more people, the z value is given by

z = (0.76 - 0.69)/0.0462493 = 1.5135

p(z > 1.5135) = 0.06507183 = 6.51%

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