Question

18% of all college students volunteer their time. Is the percentage of college students who are volunteers larger for students receiving financial aid? Of the 301 randomly selected students who receive financial aid, 72 of them volunteered their time. What can be concluded at the αα = 0.10 level of significance?

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

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

H1:H1:  ? p μ  ? ≠ > = <   (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 reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly higher than 18% at αα = 0.10, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 18%.
   • The data suggest the populaton proportion is significantly higher than 18% at αα = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 18%.
   • The data suggest the population proportion is not significantly higher than 18% at αα = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 18%.

Answer 1

). Syze Given that Sample na 301 Sample proporten for a 72 s002392 301 In the use a- test for a (upulla son - pepephon Shay qa Ho: P = 0.18 P20.18 The hypothesis. (one tailed to agains? under Ho the lest stulishe is het z = into, Tpan 6-2392 0.18 216234 Jo. 18+(1-0.18/301 = z=2.6734 P(Z <-2-6734) P-value = Plz 72-6734 0.0038 - Revelue = 0.0078 P-value = 0.0075 less than a=0.10. is resect at Qeo:10 - The dates suggest the population proportion is Sufficiently higher them 182 at 230.10. So there Sulficient evidence to conclude that the percentage of francial and recipients. who volunteer is higher than cs Scanned with CamScanner