Question

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 329 randomly selected students who receive financial aid, 39 of them volunteered their time. What can be concluded at the αα = 0.05 level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:   

H0:H0:  ? μ p  Select an answer = < > ≠   (please enter a decimal)   

H1:H1:  ? μ p  Select an answer = ≠ > <   (Please enter a decimal)

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly lower than 17% at αα = 0.05, so there is insufficient 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 αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 17%.
   • The data suggest the populaton proportion is significantly lower than 17% at αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 17%.

Answer 1

a) z-test for a population proportion

c) p-value ≤  α

d) iii) The data suggest the populaton proportion is significantly lower than 17% at αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 17%.