Recently,a case of food poisoning was traced to a particular restaurant chain.The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur.Despite the response from the restaurant chain,many consumers refused to visit the restaurant for some time after the event.A survey was conducted three months after the food poisoning occurred,with a sample of 319 former customers contacted.Of the 319 contacted,29 indicated that they would not go back to the restaurant because of the potential for food poisoning.What sample size would be needed in order to be 99 percent confident that the sample proportion is within .02 of ρ,the true proportion of customers who refuse to go back to the restaurant?
A) 14
B) 38
C) 129
D) 1,371
E) 1,777

Question

Quizplus · Accepted Answer

The sample size needed to be 99% confident that the sample proportion is within .02 of ρ, the true proportion of customers who refuse to go back to the restaurant, can be calculated using the formula:n = (Z^2 * p * q) / e^2where:n is the sample sizeZ is the z-score for the desired confidence level (99% = 2.576)p is the sample proportion (29/319 = 0.091)q is the complement of the sample proportion (1 - p = 0.909)e is the margin of error (0.02)Plugging in the values, we get:n = (2.576^2 * 0.091 * 0.909) / 0.02^2n = 1,371.04Therefore, the sample size needed is 1,371.

Recently,a Case of Food Poisoning Was Traced to a Particular