Let p be the population proportion of all L.A. County residences that have earthquake insurance.
Given : The survey revealed that only 119 of 344 randomly selected residences in Los Angeles County were protected by earthquake insurance. f
i.e.Sample size : n= 344
Sample proportion : [tex]\hat{p}=\dfrac{119}{344}\approx0.346[/tex]
Point estimate of population proportion = tex]\hat{p}=0.346[/tex]
Critical value for 99% confidence interval ( Using z-value table) :
[tex]z=2.576[/tex]
Now, the 99% confidence the proportion of all L.A. County residences that have earthquake insurance will be :
[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
i.e. [tex]0.346\pm (2.576)\sqrt{\dfrac{0.346(1-0.346)}{344}}[/tex]
i.e. [tex]0.346\pm (2.576)(0.02564)[/tex]
[tex]\approx0.346\pm 0.066=(0.346-0.066,\ 0.346+0.066)\\\\=(0.280,\ 0.412)[/tex]
We are 99% confident that the true population proportion of all L.A. County residences that have earthquake insurance lies between 0.280 and 0.412.
