Part (a) (3 points) The chair of a department at a university claims that at lea
ID: 3323443 • Letter: P
Question
Part (a) (3 points)
The chair of a department at a university claims that at least 60 percent of its students participated in a community service project in the previous semester. In order to test the claim, you collect a sample of 40 students and find that 20 of them did participate in a community service project in the previous semester. Using a level of significance of 0.05, carry out a hypothesis test for the department chair’s claim.
Part (b) (3 points)
The chair of a different department at the same university also claims that at least 60 percent of its students participated in a community service project in the previous semester. In order to test the claim of that chair, you collect a sample of 80 students and find that 40 of them did participate in a community service project in the previous semester. Using a level of significance of 0.05, carry out a hypothesis test for that department chair’s claim.
Part (c) (2 points)
Explain why we reject H0 in one of the two above parts of this question and not in the other, even though the two sample proportions are the same.
Explanation / Answer
The chair of a department at a university claims that at least 60 percent of its students participated in a community service project in the previous semester. In order to test the claim, you collect a sample of 40 students and find that 20 of them did participate in a community service project in the previous semester. Using a level of significance of 0.05, carry out a hypothesis test for the department chair’s claim.
Null Hypothesis:
H0:p<=0.6
Alterinative Hypotehsis:
Ha:p>=0.6
Alpha=0.05
Test statistic
Z=p^-p/sqrt(p(1-p)/n
P^=20/40=0.5
so z=0.5-0.6/sqrt(0.6(1-0.6)/40
=-1.291
p value=0.0984
p>0.05
Fail to reject Null hypothesis.
Accept Null hypothesis.
there is no suffiicient statistical evidence at 5% level of significance to conclude that at least 60 percent of its students participated in a community service project in the previous semester.