Respuesta :
Answer:
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{24+17}{200+150}=0.117[/tex]
Replacing the info given we got:
[tex]z=\frac{0.12-0.113}{\sqrt{0.117(1-0.117)(\frac{1}{200}+\frac{1}{150})}}=0.202[/tex]
We can calculate the p value with this probability:
[tex]p_v =P(Z>0.202)= 0.420[/tex]
Since the p value is a very higher value we don't have enough evidence to conclude that the true proportion for population 1 is higher than the trrue proportion for population 2
Step-by-step explanation:
Information given
[tex]X_{1}=24[/tex] represent the number of people with the characteristic 1
[tex]X_{2}=17[/tex] represent the number of people with the characteristic 2 [tex]n_{1}=200[/tex] sample 1 selected
[tex]n_{2}=150[/tex] sample 2 selected
[tex]p_{1}=\frac{24}{200}=0.12[/tex] represent the proportion estimated for the sample 1
[tex]p_{2}=\frac{17}{150}=0.113[/tex] represent the proportion estimated for the sample 2
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the value for the test
Hypothesis to test
We want to check if the proportion for population 1 is higher than the proportion for population 2, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} \leq p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} > p_{2}[/tex]
The statistic would be given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{24+17}{200+150}=0.117[/tex]
Replacing the info given we got:
[tex]z=\frac{0.12-0.113}{\sqrt{0.117(1-0.117)(\frac{1}{200}+\frac{1}{150})}}=0.202[/tex]
We can calculate the p value with this probability:
[tex]p_v =P(Z>0.202)= 0.420[/tex]
Since the p value is a very higher value we don't have enough evidence to conclude that the true proportion for population 1 is higher than the trrue proportion for population 2
