Respuesta :
Answer:
[tex]z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47[/tex]
Now we can calculate the p value based on the alternative hypothesis with this probability:
[tex]p_v =P(z>4.47)=0.00000391[/tex]
The p value is very low compared to the significance level of [tex]\alpha=0.05[/tex] then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24
Step-by-step explanation:
Information given
n=200 represent the random sample taken
X=75 represent the number of people Liberal
[tex]\hat p=\frac{75}{200}=0.375[/tex] estimated proportion of people liberal
[tex]p_o=0.24[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion of adults liberal is higher than 0.24:
Null hypothesis:[tex]p \leq 0.24[/tex]
Alternative hypothesis:[tex]p > 0.24[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47[/tex]
Now we can calculate the p value based on the alternative hypothesis with this probability:
[tex]p_v =P(z>4.47)=0.00000391[/tex]
The p value is very low compared to the significance level of [tex]\alpha=0.05[/tex] then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24
