1. Introduction to Statistics

A 24-hour gym is interested in whether they should purchase a new rowing machine, so they decide to survey their active members to get their opinion. They use a random number generator to obtain a sample of gym ID numbers and ask all people selected about their opinion. They can collect the data easily, as all selected respondents happen to be enrolled in fitness classes in the early afternoons. Is this a simple random sample? Is this a representative sample?

A store is interested in whether they should adjust their store hours, so they choose a random day to poll all people entering the shop and ask them if they would prefer the store to change their hours. Is this a simple random sample? Can we assume this is a representative sample?

A superintendent of a school system is interested in how the teachers working at the schools feel about the current professional development offerings, so they use the employee dashboard to randomly select 60 teachers for their survey. As it happens, approximately two teachers from each grade are chosen, and there is about the same number of teachers for each major discipline. Is this a simple random sample? Is it a representative sample?

A regional manager runs the day-to-day operations of three branches of a chain restaurant. Each location is roughly the same size and employs approximately the same number of workers. The manager is interested in streamlining policies across each location, so he decides to survey 10 random employees in each branch about certain processes. Is this a simple random sample? Is it a representative sample?