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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.

Respuesta :

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

Step-by-step explanation:

Since we  have given that

Total number of chemical companies n  = 500

Number of companies certified = 370

So, [tex]p=\dfrac{370}{500}=0.74[/tex]

At 95% level of confidence, z = 1.96

So, interval would be

[tex]p\pm z\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.74\pm 1.96\sqrt{\dfrac{0.74\times 0.26}{500}}\\\\=0.74\pm 0.038\\\\=(0.74-0.038,0.74+0.038)\\\\=(0.70, 0.778)[/tex]

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

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