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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 (((0.68*0.32) / 550)

= 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

milcah answered 6 months ago
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