Question

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 patrons 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 rho, the true proportion of customers who refuse to go back to the restaurant?

Answer 1

The simple size needed, taking into the account the pilot study and the requirements, would be 1370.

Explanation:

There is a formula we can use in order for us to determin the sample size for estimating a proportion ρ

`n=(z^(2) (Ps)(Qs))/(E^(2) )`

which is derived from the formula from the margin of error E. Here, Ps is the estimate of the true proportion of costumers who refuse to go back to the restaurant.

Ps = 29/319 = 0.0909

Qs = 1 - Ps = 0.909

E = 0.20

the z score for a confidence level of 99% is 2.575

`n=(2.575^(2) (0.0909)(0.909))/(0.02^(2) )`

n = 1370