Sale of spinach that is contaminated with e coli can cause food poisoning among consumers. A food inspector takes an SRS of 400 bags from all the bags of spinach shipped in one day. The laboratory reports that 19 of these bags had e coli contamination. Unknown to the producer, 1 percent of all bags shipped had e coli.
A statistician tells the producer that the margin of error for a 95 percent confidence statement for these data is about plus or minus 2 percentage points. The producer therefore reports that between 2.8 percent and 6.8 percent (that's 4.8 percent ± 2 percent) of all the bags of spinach are contaminated. This isn't right: only 1 percent is contaminated. What went wrong?
A) The 4.8 percent is wrong-see the answer to the previous problem for the correct estimate.
B) A 95 percent confidence statement is only right for 95 percent of all possible samples. This must be one of the 5 percent for which one gets an incorrect conclusion.
C) The 4.5 percent is correct, and it's impossible for the truth to lie outside the margin of error, so there must be another mistake. Maybe the laboratory counted contaminated bags incorrectly.

Question

Quizplus · Accepted Answer

The margin of error only accounts for random sampling error. It is possible that the sample was not truly random or that there were systematic errors in the way the bags were selected or the laboratory analysis was conducted. Therefore, it is always possible that the confidence interval does not capture the true population parameter. In this case, the margin of error was not enough to account for the discrepancy between the sample proportion and the known population proportion of contaminated bags.

Sale of Spinach That Is Contaminated with E Coli Can