Question

10% of all college students volunteer their time. Is the percentage of college students who are volunteers smaller for students receiving financial aid? Of the 322 randomly selected students who receive financial aid, 26 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 t-test for a population mean z-test for a population proportion
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 reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly lower than 10% at αα = 0.05, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 10%.
   • The data suggest the populaton proportion is significantly lower than 10% at αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 10%.
   • The data suggest the population proportion is not significantly lower than 10% at αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 10%.

Answer 1

Solution :-

Given that ,

n = 322

x = 26

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

The null and alternative hypothesis is

H0 : p = 0.10

Ha : p < 0.10

This is the left tailed test .

= x / n = 26 / 322 = 0.0807

P0 = 10% = 0.10

1 - P0 = 1- 0.10 = 0.90

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.0807 - 0.10 / [0.10 ( 1 - 0.10 ) / 322 ]

= -1.152

The test statistic = -1.152

P-value = 0.1247

= 0.05    

0.1247 > 0.05

P-value >

Fail to reject the null hypothesis .

• conclusion : - The data suggest the population proportion is not significantly lower than 10% at αα = 0.05, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 10%.