Dilbert is in charge of evaluating a new machine that manufactures shoelaces. In particular, he needs to estimate the percentage of defective shoelaces (a defective shoelace can be frayed, too short, or too long). Good machines are expected to produce no more than 1% defective products. After he evaluates 540 shoelaces, and finds that 17 are defective.
A) If Dilbert has to report a confidence interval with a margin of error equal to 1.5%, how many shoelaces should he evaluate?
B) Given the sample taht he took (in other words, do not use your answer from part A), construct BOTH a plus-four confidence interval AND a large-sample confidence interval. Which do you think it more appropriate in this particular case? Why? Note: you do not need to interpret your intervals
C) Evaluate whether the sample gives sufficient evidence to conclude that the defective rate of the machine is greater than 1%.