A company that produces socks wants to estimate the percent of the socks produced in a typical week that are

Question

A company that produces socks wants to estimate the percent of the socks produced in a typical week that are defective. A random sample of 310 socks produced in a certain week were inspected. Based on the sample, it is estimated that 12 % of all socks produced by the company in this week are defective, with an associated margin of error of 3.62 % . Based on the estimate and associated margin of error, which of the following is the most appropriate conclusion about all socks produced by the company during this week?

Accepted Answer

Choice B is correct. It&rsquo;s given that, based on the sample, an estimate of 12 % of all socks produced by the company in a certain week are defective, with an associated margin of error of 3.62 % . This estimate, plus or minus the margin of error, gives an interval of plausible values for the actual percent of all socks produced by the company that week that are defective. Subtracting 3.62 % from 12 % yields 8.38 % . Adding 3.62 % to 12 % yields 15.62 % . Therefore, it is plausible that between 8.38 % and 15.62 % of all socks produced by the company are defective. Choice A is incorrect and may result from conceptual errors. Choice C is incorrect. 12 % is the estimated percent of defective socks based on the sample. However, since the margin of error for this estimate is known, the most appropriate conclusion is not that the percent of defective socks is exactly 12 % but instead that it lies in an interval of plausible percents. Choice D is incorrect and may result from conceptual errors.

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