Respuesta :
Answer:
Option b - not significantly greater than 75%.
Step-by-step explanation:
A random sample of 100 people was taken i.e. n=100
Eighty of the people in the sample favored Candidate i.e. x=80
We have used single sample proportion test,
[tex]p=\frac{x}{n}[/tex]
[tex]p=\frac{80}{100}[/tex]
[tex]p=0.8[/tex]
Now we define hypothesis,
Null hypothesis [tex]H_0[/tex] : candidate A is significantly greater than 75%.
Alternative hypothesis [tex]H_1[/tex] : candidate A is not significantly greater than 75%.
Level of significance [tex]\alpha=0.05[/tex]
Applying test statistic Z -proportion,
[tex]Z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}[/tex]
Where, [tex]\widehat{p}=80\%=0.80[/tex] and [tex]p=75%=0.75[/tex]
Substitute the values,
[tex]Z=\frac{0.80-0.75}{\sqrt{\frac{0.75(1-0.75)}{100}}}[/tex]
[tex]Z=\frac{0.80-0.75}{\sqrt{\frac{0.1875}{100}}}[/tex]
[tex]Z=\frac{0.05}{0.0433}[/tex]
[tex]Z=1.1547[/tex]
The p-value is
[tex]P(Z>1.1547)=1-P(Z<1.1547)[/tex]
[tex]P(Z>1.1547)=1-0.8789[/tex]
[tex]P(Z>1.1547)=0.1241[/tex]
Now, the p-value is greater than the 0.05.
So we fail to reject the null hypothesis and conclude that the A is not significantly greater than 75%.
Therefore, Option b is correct.
