Respuesta :
Answer:
[tex]z=\frac{0.384-0.362}{\sqrt{0.374(1-0.374)(\frac{1}{4276}+\frac{1}{3908})}}=2.055[/tex]
The p value can be calculated from the alternative hypothesis with this probability:
[tex]p_v =2*P(Z>2.055)=0.0399[/tex]
And the best option for this case would be:
C. between 0.01 and 0.05.
Step-by-step explanation:
Information provided
[tex]X_{1}=1642[/tex] represent the number of smokers from the sample in 1995
[tex]X_{2}=1415[/tex] represent the number of smokers from the sample in 2010
[tex]n_{1}=4276[/tex] sample from 1995
[tex]n_{2}=3908[/tex] sample from 2010
[tex]p_{1}=\frac{1642}{4276}=0.384[/tex] represent the proportion of smokers from the sample in 1995
[tex]p_{2}=\frac{1415}{3908}=0.362[/tex] represent the proportion of smokers from the sample in 2010
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic
[tex]p_v[/tex] represent the value for the pvalue
System of hypothesis
We want to test the equality of the proportion of smokers and the system of hypothesis are:
Null hypothesis:[tex]p_{1} = p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]
The statistic is 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{1642+1415}{4276+3908}=0.374[/tex]
Replacing the info given we got:
[tex]z=\frac{0.384-0.362}{\sqrt{0.374(1-0.374)(\frac{1}{4276}+\frac{1}{3908})}}=2.055[/tex]
The p value can be calculated from the alternative hypothesis with this probability:
[tex]p_v =2*P(Z>2.055)=0.0399[/tex]
And the best option for this case would be:
C. between 0.01 and 0.05.
