4. For each of the scenarios below, determine if the sample is a simple random s

Question

4. For each of the scenarios below, determine if the sample is a simple random sample from the population of interest, or if the sample has some form of bias. If there is a bias, describe the nature of the bias ina sentence or two. (a) You are interested in the avcrage height of all freshmen on the UW-Madison campus. You draw a simple random sample of freshmen in your statisties class. (b) You are interested in the rage of the glaze thicknesses on mugs created in a factory. Yon sample every 5th mug off of the assembly line. (c) You are interested in the average IQ of Gth graders in Dane County publie schools. You get your sample by using computer software to randomly select 100 6th grade student ID numbers from the Dane County public school database (d) You work for a doctor's office and you are interested in estimating the proportion of patients that visited the office n the last month that feel they received satisfactory care. You randomly select names from the list of patients who have been to the office and email them a survey. About 25% of the surveys are returned

Explanation / Answer

a)

The sample will have a bias. If the population is all freshmen on the UW-Madison campus, then a sample that contains students only from the statistics class would be representative of all the freshmen in the statistics class but will not be representative of all the freshmen on campus.

b)

This is a simple random sample and should not be having any bias.

c)

This is a simple random sample and should not be having any bias.

d)

This sample might contain some form of bias. Generally, a common fact is that people who normally have an issue with the service will make it a point to give their feedback and make their negative concerns known whereas people who are satisfied don't normally fill surveys or find it important to give their feedback. Thus, the sample 25% of the surveys returned might contain a larger proportion of negative feedback than actually exists in the population. Therefore, the collector of the survey should be prepared for a larger proportion of negative feedback and adjust his calcuations accordingly.

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