According to a recent​ report, 44% of college student internships are unpaid. A recent survey of 100 college interns at a local university found that 49 had unpaid internships.

Question

a. Use the​ five-step p-value approach to hypothesis testing and a

0.01

level of significance to determine whether the proportion of college interns that had unpaid internships is different from

0.44.

b. Assume that the study found that

59

of the

100

college interns had unpaid internships and repeat​ (a). Are the conclusions the​ same?

QUESTION: WHAT IS THE ZSTAT? _____

Answer 1

Ho: p = 0.44

Ha: p != 0.44

a)

sample proportion (phat) = 49/100 = 0.49

sample size (n) = 100

z = (phat - p)/sqrt(p * (1-p)/n) = (0.49 - 0.44)/sqrt(0.44 * 0.56/100) = 1.01

for a two sided test:

p-value = P(z > 1.01) + P(z < -1.01)

since normal distribution is symmetric that is the same as 2 * P(z < -1.01)

P(z < -1.01) = 0.1562, so p-value is 0.3124.

since p-value > alpha (0.01), we cannot reject Ho and conclude any differences

b) here phat = 59/100 = 0.59

z = (0.59 - 0.44)/sqrt(0.44 * 0.56/100) = 3.02

p-value = 2*( P(z < -3.02) = 0.0013

since p-value < alpha, we can reject Ho and conclude differences