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In a certain country, pesticide T is used for controlling insects that are harmful to crops. According to standards set by government, drinking water wells with level of pesticide T above 1 part per billion are considered contaminated. A study has been conducted by the Environmental Protection Department (EPD) which has selected a random sample of 250 wells and tested them, and it is found that 50 wells are contaminated
(a) Construct a 90% confidence interval for the true proportion of wells contaminated with pesticide T in the country. State the condition(s) required for this confidence interval to be valid?
(b) How large a sample is required if the EPD wants to be 95% confident that the estimation error is within ±0.01?
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