Question

If you live in California, the decision to purchase earthquake insurance is a critical one. An article in the Annals of the Association of American Geographers investigated many factors that California residents consider when purchasing earthquake insurance. The survey revealed that only 119 of 344 randomly selected residences in Los Angeles County were protected by earthquake insurance. Estimate with 99% confidence the proportion of all L.A. County residences that have earthquake insurance.

Answer 1

Answer with explanation:

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 :
`\hat{p}=(119)/(344)\approx0.346`

Point estimate of population proportion = tex]\hat{p}=0.346[/tex]

Critical value for 99% confidence interval ( Using z-value table) :

`z=2.576`

Now, the 99% confidence the proportion of all L.A. County residences that have earthquake insurance will be :

`\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

i.e.
`0.346\pm (2.576)\sqrt{(0.346(1-0.346))/(344)}`

i.e.
`0.346\pm (2.576)(0.02564)`

`\approx0.346\pm 0.066=(0.346-0.066,\ 0.346+0.066)\\\\=(0.280,\ 0.412)`

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.