$17 \%$ of all college students volunteer their time. Is the percentage of college students who are volunteers smaller for students receiving financial aid? Of the 332 randomly selected students who receive financial aid, 40 of them volunteered their time. What can be concluded at the $\alpha=0.10$ level of significance?
a. For this study, we should use z-test for a population proportion
b. The null and alternative hypotheses would be:
\[
H_{0}: \overbrace{}^{\vee}=.17 \quad \checkmark \text { (please enter a decimal) }
\]
$0^{\circ}$
$0^{s}$
$0^{s}$
\[
H_{1}: \mathrm{p}^{\checkmark}< .17 \quad \checkmark \text { (Please enter a decimal) }
\]
$0^{s}$
$0^{\infty}$
$0^{\circ}$
c. The test statistic $z \sim^{\vee}=$ (please show your answer to 3 decimal places.)
$0^{8}$
d. The $p$-value $=$ (Please show your answer to 4 decimal places.)
e. The $p$-value is $\alpha$
f. Based on this, we should
reject the null hypothesis.
g. Thus, the final conclusion is that ...
The data suggest the populaton proportion is significantly lower than $17 \%$ at $\alpha=0.10$, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than $17 \%$.
The data suggest the population proportion is not significantly lower than $17 \%$ at $\alpha=0.10$, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to $17 \%$.

The data suggest the population proportion is not significantly lower than $17 \%$ at $\alpha=0.10$, so there is insufficient evidence to conclude that the percentage of financial aid recipients who

Step 1 ：Calculate the sample proportion of students who volunteer their time by dividing the number of students who volunteer their time by the total number of students.

Step 2 ：Perform a hypothesis test to determine if the proportion of students who volunteer their time is significantly less than 17%. The null hypothesis is that the proportion is equal to 17%, and the alternative hypothesis is that the proportion is less than 17%.

Step 3 ：Use a z-test for a population proportion to perform this hypothesis test. The test statistic is calculated as follows: \[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\] where \(\hat{p}\) is the sample proportion, \(p_0\) is the population proportion under the null hypothesis, and \(n\) is the sample size.

Step 4 ：Calculate the p-value, which is the probability of observing a test statistic as extreme as the one we calculated, assuming the null hypothesis is true. If the p-value is less than the significance level \(\alpha\), we reject the null hypothesis.

Step 5 ：Given that n = 332, x = 40, p0 = 0.17, and alpha = 0.1, we find that \(\hat{p}\) = 0.12048192771084337, z = -2.4019793226489847, and p_value = 0.008153315068446637.

Step 6 ：Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. This means that there is sufficient evidence to conclude that the proportion of students who receive financial aid and volunteer their time is less than 17%.

Step 7 ：\(\boxed{\text{Final Answer:}}\) The test statistic is \(z \approx -2.402\) and the p-value is \(p \approx 0.0082\). Since the p-value is less than the significance level of \(\alpha = 0.10\), we reject the null hypothesis. Therefore, there is sufficient evidence to conclude that the proportion of students who receive financial aid and volunteer their time is less than 17%. Thus, the final conclusion is that the data suggest the population proportion is significantly lower than 17% at \(\alpha=0.10\), so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 17%.