MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

Answer with explanation:Let p be the proportion of all L.A. County residences that have earthquake insurance. Given : The survey revealed that only 141 of 345 randomly selected residences in Los Angeles County were protected by earthquake insurance.i.e. n= 345Sample Proportion : [tex]\hat{p}=\dfrac{141}{345}\approx0.409[/tex]Critical value for 90% confidence interval : [tex]z_c=1.645[/tex]Formula to find the confidence interval for population proportion : [tex]\hat{p}\pm z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex][tex]0.409\pm (1.645)\sqrt{\dfrac{0.409(1-0.409)}{345}}\\\\\approx0.409\pm 0.044\\\\=(0.409-0.044, \ 0.409+0.044)\\\\=(0.369,\ 0.453)[/tex]Hence, the 90% confidence the proportion of all L.A. County residences that have earthquake insurance = (0.369, 0.453)Interpretation : We are 90% confident that the true proportion of all L.A. County residences that have earthquake insurance lies between 0.369 and 0.453 .