Give an alternative proof of Proposition 13.1 in which you use list counting instead of subset counting.

Chapter 1 Notes Section 1.1 Sampling ● Statistics ○ Collecting data, displaying data and drawing conclusions ● Population: ○ The entire collection (ex: Clemson University) ● Sample: ○ Subset of the population (ex: Athletes at Clemson) ● Sample Types ○ Simple Random Sample (SRS): everything has an equal chance of being selected (ex: lottery) ○ Stratified Sample: population divided into groups that are similar then from the groups a SRS is taken ○ Cluster Sample: grouped into categories then pick one whole group to sample ○ Systematic Sample: items are ordered then decided how frequently to pick items (ex: every 5th item) ○ Voluntary Sample: asking people to give you an opinion; not reliable ● Statistics and Parameters ○ Statistic: describes a sample ○ Parameter: describes a population Section 1.2 Types of Data ● Information is collected on individuals (ex: people, places, animals, etc) ● The characteristic of the data collected is considered the variable (ex: hair color, race, political views, gender, etc) ● Values of the variables are the data ● Quantitative and Qualitative Variables ○ Quantitative Variables: numeric values (ex: height, goals scored, etc) ■ Discrete: can be listed (ex: number of fouls in a game)