Question 22 of my final exam for Design and Analysis of Sample Surveys

22. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. Three stores are selected at random and are checked: the percent of spoiled vegetables are 3%, 5%, and 10% in the three stores. Give an estimate and standard error for the percentage of spoiled vegetables for the entire chain.

Solution to question 21

From yesterday:

21. A country is divided into three regions with populations of 2 million, 2 million, and 0.5 million, respectively. A survey is done asking about foreign policy opinions. Somebody proposes taking a sample of 50 people from each reason. Give a reason why this non-proportional sample would not usually be done, and also a reason why it might actually be a good idea.

Solution: Nonproportional sampling is usually avoided because it makes the analysis more complicated and it results in a higher standard error for estimates of the general population. It might be a good idea here if there is a goal of comparing the different regions.

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