Question

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 60 had unpaid internships.

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 50 of the 100 college interns had unpaid internships and repeat​ (a). Are the conclusions the​ same?

Answer 1

Answer;

a)

Given,

sample proportion p^ = x/n = 60/100 = 0.60

Ho ; p = 0.44

Ha : p != 0.44

test statistic z = (p^ - p)/sqrt(pq/n)

substitute values

= (0.60 - 0.44) / sqrt(0.60*0.40/100)

= 3.27

P value = 0.0010755 [since from z table]

= 0.001

Here p value < alpha, so we reject Ho.

So there is sufficient evidence to support the claim.

b)

sample proportion p^ = x/n = 50/100 = 0.5

test statistic z = (p^ - p)/sqrt(pq/n)

substitute values

= (0.50 - 0.44) / sqrt(0.50*0.50/100)

= 1.2

P value = 0.2301393 [since from z table]

= 0.2301

Here p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.