Respuesta :
Answer:
Null Hypothesis:-H₀: P = 0.12
There is no difference between the percentage of volunteers selected from the college students.
Alternative Hypothesis:-H₁: P ≠ 0.12
There is a difference between the percentage of volunteers selected from the college students.
The calculated value Z = 0.5543 < 2.376 at 0.01 level of significance
The null hypothesis is accepted
There is a difference between the percentage of volunteers selected from the college students.
Step-by-step explanation:
Step(i):-
Given that the Population proportion P= 12% = 0.12
Given that the 331 randomly selected students who receive financial aid, 43 of them volunteered their time.
Sample proportion
[tex]p = \frac{x}{n} = \frac{43}{331} = 0.1299[/tex]
Step(ii):-
Null Hypothesis:-H₀: P = 0.12
There is a difference between the percentage of volunteers selected from the college students.
Alternative Hypothesis:-H₁: P ≠ 0.12
There is no difference between the percentage of volunteers selected from the college students.
Step(iii):-
Test statistic
[tex]Z = \frac{p-P }{\sqrt{\frac{PQ}{n } } }[/tex]
[tex]Z = \frac{0.1299-0.12 }{\sqrt{\frac{(0.12)(0.88)}{331 } } }[/tex]
Z = 0.5543
Level of significance = 0.01
Critical value Z₀.₀₁ = 2.376
Final answer:-
The calculated value Z = 0.5543 < 2.376 at 0.01 level of significance
The null hypothesis is accepted
There is a difference between the percentage of volunteers selected from the college students.