Question

In country​ A, the vast majority​ (90%) of companies in the chemical industry are ISO 14001 certified. The ISO 14001 is an international standard for environmental management systems. An environmental group wished to estimate the percentage of country​ B's chemical companies that are ISO 14001 certified. Of the

500500

chemical companies​ sampled,

340340

are certified.

​a) What proportion of the sample reported being​ certified?

​b) Create a

9090​%

confidence interval for the proportion of country​ B's chemical companies with ISO 14001 certification.​ (Be sure to check​ conditions.) Compare to the country A proportion.

​a) The sample proportion is

. 68.68.

​(Type an integer or a​ decimal.)

​b) What is the confidence​ interval? Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice.

A.The

9090​%

confidence interval is

left parenthesis nothing % comma nothing % right parenthesis%,%.

​(Round to one decimal place as​ needed.)

B.

The conditions of a confidence interval are not satisfied.

Answer 1

(a)

340/500 = 0.68

(b)

n = 500    

p = 0.68    

% = 90    

Standard Error, SE = √{p(1 - p)/n} =    √(0.68(1 - 0.68))/500 = 0.020861448

z- score = 1.644853627    

Width of the confidence interval = z * SE =     1.64485362695147 * 0.0208614476966485 = 0.03431403

Lower Limit of the confidence interval = P - width =     0.68 - 0.0343140279072907 = 0.64568597

Upper Limit of the confidence interval = P + width =     0.68 + 0.0343140279072907 = 0.71431403

The 90% confidence interval is [0.6, 0.7]