Small Sample Size

The dataset imagpop contains information about 10000 people from an imaginary population. One of the variables is math, which indicates whether the individual was a mathematics major. You can see the distribution of math majors in the population in the row percents shown below:

rowPerc(xtabs(~math,data=imagpop))

## no yes Total
## 95.37 4.63 100.00

Suppose you were interested in the following

Research Question: Are quantitative skills an important part of your job?

You decide to quickly take a simple random sample of size 10 from this population. You can see the distribution of math majors in the sample below:

set.seed(2014)
smallsamp<-popsamp(n=10,pop=imagpop)
rowPerc(xtabs(~math,data=smallsamp))

## no yes Total
## 100 0 100

Which of the following statements best describes a problem that may arise in this scenario?

Group of answer choices

( ) The sampled individuals that were selected might all have jobs that require quantitative skills. This could introduce bias into the results because most jobs do not require quantitative skills.

( ) Since 100% of the individuals in the sample are not math majors, this sample is not representative of the population. About 5% of the population are math majors. Our sample should reflect this distribution. This introduces bias into the results.

( ) This was not really a simple random sample because an individual who was not a math major has a greater chance of being selected to be part of the sample than an individual who was a math major.

( ) The researchers decided which individuals were part of the sample. This is an example of quota sampling. This introduces bias in the results because researchers may have chosen a group of people that are not representative of the population, even if this was done unintentionally.

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Given that the dataset contains 10000 people from an imaginary population in which math is a variable. This variable indicates whether an individual was a mathematics major or not.

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