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? a 3.62% of the socks are defective. b it is plausible that between 8.38% and 15.62% of the socks are defective. c 12% of the socks are defective. d it is plausible that more than 15.62% of the socks are defective.

Explanation:

Step1: Recall margin - of - error concept

The margin of error gives a range around the sample estimate.

Step2: Calculate the lower and upper bounds

The sample estimate of defective socks is 12% and the margin of error is 3.62%. The lower bound is $12 - 3.62=8.38\%$ and the upper bound is $12 + 3.62 = 15.62\%$. This means that the true proportion of defective socks in the population is likely to be within this range.

Answer:

B. It is plausible that between 8.38% and 15.62% of the socks are defective.