18% of all college students volunteer their time. Is the percentage of college students who are volunteers smaller for students receiving financial aid? Of the 310 randomly selected students who receive financial aid, 50 of them volunteered their time. What can be concluded at the α = 0.05 level of significance?
For this study, we should use a z-test for a population proportion.
The null and alternative hypotheses would be:
H0: p = 0.18
H1: p < 0.18
The test statistic z = -2.121 (please show your answer to 3 decimal places.)
The p-value = 0.0175 (Please show your answer to 4 decimal places.)
The p-value is ≤ α.
Based on this, we should reject the null hypothesis.
Thus, the final conclusion is that the data suggest the population proportion is significantly lower than 18% at α = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 18%.