Question

12% of all college students volunteer their time. Is the percentage of college students who are volunteers different for students receiving financial aid? Of the 336 randomly selected students who receive financial aid, 24 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:  ? μ p  ? > < ≠ =   (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 accept reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton proportion is significantly different from 12% at αα = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is different from 12%.
   • The data suggest the population proportion is not significantly different from 12% at αα = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 12%.
   • The data suggest the population proportion is not significantly different from 12% at αα = 0.10, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is different from 12%.

Answer 1

a)

For this study, we should use Select an answer z-test for a population proportion
b)

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.12
Alternative Hypothesis: p ≠ 0.12

c)

P = 24/336 = 0.0714

Test statistic,
z= (P -p)/sqrt(p*(1-p)n)
= ( 0.0714 - 0.12)/sqrt(0.12*(1-0.12)/336)
= -2.741

d)

P-value Approach
P-value = 0.0061

e)
As P-value < = alpha,

f)

reject null hypothesis.

g)

The data suggest the populaton proportion is significantly different from 12% at αα = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is different from 12%.