I do have the solution but they do not provide every singlestep so I do want to

Question

I do have the solution but they do not provide every singlestep so I do want to know the every
single steps..
The solution for a) 0.319< p< 0.445
                        b) E - 0.06
thank you in advance..
In a sample survey of the "safety explosives" used in certainmining operations, explosives containing potassium nitrate werefound to be used in 95 of 250 cases a) use 95% confidence interval for the corresponding trueproportion b)if 95/250 = 0.38 is used as an estimate of the correspondingtrue proportion, what can we say with 95% confidence about themaximum error? I do have the solution but they do not provide every singlestep so I do want to know the every single steps.. The solution for a) 0.319< p< 0.445                         b) E - 0.06 thank you in advance..
In a sample survey of the "safety explosives" used in certainmining operations, explosives containing potassium nitrate werefound to be used in 95 of 250 cases a) use 95% confidence interval for the corresponding trueproportion b)if 95/250 = 0.38 is used as an estimate of the correspondingtrue proportion, what can we say with 95% confidence about themaximum error?

Explanation / Answer

(a) p=95/250=0.38 =0.05, |Z(0.025)|=1.96 (check normal table) The 95% CI is p±Z*p*(1-p)/n --> 0.38 ± 1.96*sqrt(0.38*(1-0.38)/250) --> ( 0.319, 0.440) (b) the maximum error is E= 1.96*p*(1-p)/n =1.96*sqrt(0.38*(1-0.38)/250) =0.06

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