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 500 chemical companies​ sampled, 370 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.

Answer 1

Answer: a) 0.74, b) (0.70, 0.778)

Explanation:

Since we have given that

Total number of chemical companies n = 500

Number of companies certified = 370

So,
`p=(370)/(500)=0.74`

At 95% level of confidence, z = 1.96

So, interval would be

`p\pm z\sqrt{(p(1-p))/(n)}\\\\=0.74\pm 1.96\sqrt{(0.74* 0.26)/(500)}\\\\=0.74\pm 0.038\\\\=(0.74-0.038,0.74+0.038)\\\\=(0.70, 0.778)`

Hence, a) 0.74, b) (0.70, 0.778)