Question
In: Math
In country A, the vast majority (90%) of companies in the chemical industry are ISO 14001...
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 550 chemical companies sampled, 374 are certified.
a) What proportion of the sample reported being certified?
b) Create a 95% 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.
Solutions
Expert Solution
Solution :
Given that,
n = 550
x = 374
(a)
Point estimate = sample proportion = 
= x / n = 374/550=0.68
1 -
= 1-0.68=0.32
(B)
At 95% confidence level
= 1 - 95%
=1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96
Margin of error = E = Z
/ 2 * 
* (1 -
)) / n)
= 1.96 (
= 0.039
A 95% confidence interval s ,
- E < p <
+ E
0.68-0.039 < p <0.68+0.039
0.641< p < 0.719
5% confidence interval for the proportion of country B's chemical companies with ISO 14001 certification 0.641 , 0.719
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