Respuesta :
Answer:
[tex]z=\frac{0.3867 -0.32}{\sqrt{\frac{0.32(1-0.32)}{225}}}=2.145[/tex]
For a bilateral test the p value would be:
[tex]p_v =2*P(z>2.145)=0.0320[/tex]
Step-by-step explanation:
Information given
n=225 represent the sample selected
X=87 represent the households with incomes below the poverty level
[tex]\hat p=\frac{87}{225}=0.3867[/tex] estimated proportion of households with incomes below the poverty level
[tex]p_o=0.32[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to check if the true proportion is equal to 0.32 or not.:
Null hypothesis:[tex]p=0.32[/tex]
Alternative hypothesis:[tex]p \neq 0.32[/tex]
The statistic is given bY:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.3867 -0.32}{\sqrt{\frac{0.32(1-0.32)}{225}}}=2.145[/tex]
For a bilateral test the p value would be:
[tex]p_v =2*P(z>2.145)=0.0320[/tex]