# Corrected Solutions to Learn By Doing - Sampling (Software)

## Part A

Different random samples will yield different results, but the summaries should be roughly the same for population and sample.
Here is the result from one possible random sample:
- The percentage of right-handed students is 86.71% in the population and it was 85.94% in our random sample; close enough
to assert that there is no bias.
- The percentage of females is 62.09% in the population and 67.19% in our random sample; there is no clear evidence of
bias.
- The SAT Verbal scores averaged 588.78 for the population and 592.61 for our random sample; again, there is no clear
evidence of bias.
- Finally, median age for the population is 19.67 and 19.67 for our random sample; there is no evidence of any bias
at all.

## Part B

- Handed—should be representative. Business students shouldn't be any different from other students with respect
to this variable.
- Sex—could easily be biased. We expect fewer women in business than in the social or natural sciences.
- Verbal—could easily be biased. Business students' SAT Verbal scores may tend to be lower, since there are likely
to be fewer women, and women tend to do better on the verbal portion of the SAT (as the background to this
problem suggests).
- Age—should be representative. Regardless of major, students may take introductory statistics at about the same
point in their college career (as suggested by the background).

## Part C

- The percentage of right-handed students is 86.71% in the population and it was 90.63% in the sample of business students;
close enough to assert that there is no clear bias.
- The percentage of females is 62.09% in the population and 52.08% in the sample of business students; apparently biased,
in that females are under-represented in business statistics.
- The SAT Verbal score averaged 588.78 for the population and 574.65 for the business students; the sample does seem
to be biased, due to lower SAT Verbal scores for business students.
- Finally, the median age for the population is 19.7 and our sample of business students had a median age of 19.5
years; apparently the business students may be considered an unbiased sample when it comes to age.