Question

19% of all college students volunteer their time. Is the percentage of college students who are volunteers larger for students receiving financial aid? Of the 308 randomly selected students who receive financial aid, 65 of them volunteered their time. What can be concluded at the α = 0.01 level of significance?

a. For this study, we should use: Z-test for a population proportion or t-test for a population mean?

b. The null and alternative hypotheses would be:

H 0 : (p μ) (≠ < > =)  ____ (please enter a decimal)

H 1 : (p μ) ( ≠ < > =) ____  (Please enter a decimal)

c. The test statistic (t z) = ____ (please show your answer to 3 decimal places.)

d. The p-value = ______ (Please show your answer to 4 decimal places.)

e. The p-value is?  (> ≤) α

f. Based on this, we should (accept, reject, fail to reject)  the null hypothesis.

g. Thus, the final conclusion is that ...

- The data suggest the populaton proportion is significantly higher than 19% at α α = 0.01, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 19%.

- The data suggest the population proportion is not significantly higher than 19% at α α = 0.01, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 19%.

- The data suggest the population proportion is not significantly higher than 19% at α α = 0.01, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 19%.

Answer 1

Given that,
possibile chances (x)=65
sample size(n)=308
success rate ( p )= x/n = 0.211
success probability,( po )=0.19
failure probability,( qo) = 0.81
null, Ho:p=0.19
alternate, H1: p>0.19
level of significance, α = 0.01
from standard normal table,right tailed z α/2 =2.326
since our test is right-tailed
reject Ho, if zo > 2.326
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.21104-0.19/(sqrt(0.1539)/308)
zo =0.941
| zo | =0.941
critical value
the value of |z α| at los 0.01% is 2.326
we got |zo| =0.941 & | z α | =2.326
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.9412 ) = 0.1733
hence value of p0.01 < 0.1733,here we do not reject Ho
ANSWERS
---------------
a.
Z-test for a population proportion
b.
null, Ho:p=0.19
alternate, H1: p>0.19
c.
test statistic: 0.941
critical value: 2.326
d.
p-value: 0.1733
e.
p value is greater than alpha value
f.
decision: do not reject Ho
g.
we do not have enough evidence to support the claim that the populaton proportion is significantly higher than 19%