In response to nutrition concerns raised last year about food served in school c

Question

In response to nutrition concerns raised last year about food served in school cafeterias, the Smallville School District entered into a one-year contract with the Healthy Alternative Meals (HAM) company. Under this contract the company plans and prepares meals for 30000 elementary, middle, and high school students, with a focus on good nutrition. The school administration would like to survey the students in the district to estimate the proportion of students who are satisfied with the food under this contract. Two sampling plans for selecting the students to be surveyed are under consideration by the administration. One plan is to take a simple random sample of students in the district and then survey those students. The other plan is to take a stratified random sample of students in the district and then survey those students the 30000 students in the district. stratify in this survey. Explain your reasoning. context of this study (a) Describe a simple random sampling procedure that the administrators could use to select 200 students from (b) If a stratified random sampling procedure is used, give one example of an effective variable on which teo (c) Describe one statistical advantage of using a stratified random sample over a simple random sample in the (d) Suppose a simple random sampling procedure was used and the results obtained were as follows 25 Represent the result of the survey by an appropriate graphlie

Explanation / Answer

a)

The administrators could number an alphabetical list of students from 0001 to 30000. They could then use a random number generator from a calculator or computer to generate 200 unique random numbers from 0001 to 30000. The students corresponding to those 200 numbers would be asked to participate in the survey.

b)

One could stratify by the school level of the student (elementary, middle, high school). We would do this because the different age levels may have differing opinions about school cafeteria food.

c)

One statistical advantage is that stratified random sampling as opposed to simple random sampling is, for example, if the elementary, middle and high strata create groups that differ with respect to what they value and therefore more homogeneous with respect to opinion on this issue then for the same overall sample size a more accurate estimate of the overall proportion of students who are satisfied with the food under this contract may result.

Another advantage is that stratified random sampling guarantees that each of the school-level strata will have some representation, because it is possible that a simple random sample would miss one or more of the strata completely.

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