Question

A bank randomly selected 253 checking account customers and found that 112 of them also had savings accounts at this same bank. Construct a 99% confidence interval for the true proportion of checking account customers who also have savings accounts. (Give your answers correct to three decimal places.)

Lower Limit_______

Upper Limit_______

You may need to use the appropriate table in Appendix B to answer this question.

Answer 1

n = 253    

p = 112/253 = 0.442687747    

% = 99    

Standard Error, SE = √{p(1 - p)/n} =    √(0.442687747035573(1 - 0.442687747035573))/253 = 0.031227541

z- score = 2.575829304    

Width of the confidence interval = z * SE =     2.57582930354892 * 0.0312275409039785 = 0.08043681

Lower Limit of the confidence interval = P - width =     0.442687747035573 - 0.0804368149382402 = 0.362

Upper Limit of the confidence interval = P + width =     0.442687747035573 + 0.0804368149382402 = 0.523

The 99% confidence interval is [0.362, 0.523]