Question

According to a recent​ report, 47% of college student internships are unpaid. A recent survey of 100 college interns at a local university found that 52 had unpaid internships.

a. Use the​ five-step p-value approach to hypothesis testing and a 0.10 level of significance to determine whether the proportion of college interns that had unpaid internships is different from 0.47.

b. Assume that the study found that 59 of the 100 college interns had unpaid internships and repeat​ (a). Are the conclusions the​ same?

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.47
Alternative Hypothesis, Ha: p ≠ 0.47

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.52 - 0.47)/sqrt(0.47*(1-0.47)/100)
z = 1

P-value Approach
P-value = 0.3173

As P-value >= 0.1, fail to reject null hypothesis.

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.47
Alternative Hypothesis, Ha: p ≠ 0.47

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.59 - 0.47)/sqrt(0.47*(1-0.47)/100)
z = 2.4

P-value Approach
P-value = 0.0164
As P-value < 0.1, reject the null hypothesis.

the conclusion are different