Five years ago,a company found that 8% of its employees commuted to work by car.A test for the current proportion of commuting employees was done on a random sample of 1000 employees,and found car commuting to be 12%.Create a 95% confidence interval for the proportion of employee commute by car.

A) Based on the data,we are 95% confident the proportion of employee commute by car is between 8% and 16%.
B) Based on the data,we are 95% confident the proportion of employee commute by car is between 4.64% and 19.36%.
C) Based on the data,we are 95% confident the proportion of employee commute by car is between 6.32% and 13.68%.
D) Based on the data,we are 95% confident the proportion of employee commute by car is between 9.99% and 14.01%.
E) Based on the data,we are 95% confident the proportion of employee commute by car is between 6.32% and 9.68%.

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Kaitlyn Flint · Accepted Answer

Final Answer : D, Explanation :   To calculate a 95% confidence interval for the proportion, we use the formula:   p ^ ± Z p ^ ( 1 − p ^ ) n \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} p ^ ​ ± Z n p ^ ​ ( 1 − p ^ ​ ) ​ ​  , where   p ^ = 0.12 \hat{p} = 0.12 p ^ ​ = 0.12  ,   Z = 1.96 Z = 1.96 Z = 1.96   for 95% confidence, and   n = 1000 n = 1000 n = 1000  . Plugging these values in, we get   0.12 ± 1.96 0.12 ( 0.88 ) 1000 0.12 \pm 1.96 \sqrt{\frac{0.12(0.88)}{1000}} 0.12 ± 1.96 1000 0.12 ( 0.88 ) ​ ​  , which simplifies to   0.12 ± 0.02001 0.12 \pm 0.02001 0.12 ± 0.02001  , or an interval from   9.99 % 9.99\% 9.99%   to   14.01 % 14.01\% 14.01%  .

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