Question

15% of all college students volunteer their time. Is the percentage of college students who are volunteers larger for students receiving financial aid? Of the 354 randomly selected students who receive financial aid, 60 of them volunteered their time. What can be concluded at the α = 0.10 level of significance? For this study, we should use The null and alternative hypotheses would be: H 0 : (please enter a decimal) H 1 : (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly higher than 15% at α = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 15%. The data suggest the population proportion is not significantly higher than 15% at α = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 15%. The data suggest the population proportion is not significantly higher than 15% at α = 0.10, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 15%.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.15
Alternative Hypothesis, Ha: p > 0.15

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.28.
Hence reject H0 if z > 1.28

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1695 - 0.15)/sqrt(0.15*(1-0.15)/354)
z = 1.027

P-value Approach
P-value = 0.1522
As P-value >= 0.1, fail to reject null hypothesis.

The data suggest the population proportion is not significantly higher than 15% at α = 0.10, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is higher than 15%.