Probability and Statistical Inference

1. Define a parameter as a characteristic of a population that one is interested in. 
2. Describe that an experiment is when a “treatment” is assigned to some subjects and not to others for the purpose of seeing what effect the treatments may have on a sample or population. 
3. Describe that an observational study records data when an independent variable is not directly manipulated. 
4. Describe that a sample survey is a type of observational study where the data is collected by asking people to respond to a set of questions about a population characteristic. 
5. Describe that random selection when using an observational study and survey is important to the validity of the data collected and that random assignment of treatment and control is important to the validity of the data in an experiment. 
6. Describe that because there are multiple factors that may contribute to a parameter, sample surveys and observational studies cannot determine causality, only correlation.
7. Describe good and bad characteristics of a study design along with potential implications of those design choices.

• This is a pretty text-heavy lesson; however, it is very important for students to understand the idea that the strength of the statistical analysis is based on how the data was collected. If there is bias in the method of collection of data, then the statistical analysis is invalid (like the saying “garbage in, garbage out”). 
• If there is an opportunity to introduce the idea of multiple samples, repeatedly drawn of similar sizes being used to collect information, this would help student understanding of lesson 11.

Is each of the following an observational study or an experiment? Explain your answer. 

If it is an experiment, identify the treatment variable and the response variable in the context of the problem. If it is an observational study, identify the population of interest. 

1. A study is done to see how high soda will erupt when mint candies are dropped into two-liter bottles of soda. You want to compare one mint candy, five minute candies, and ten mint candies. You design a cylindrical mechanism that drops the desired number of mint candies all at once. You have 15 bottles of soda to use. You randomly assign five bottles into which you drop one candy, five into which you drop five candies, and five into which you drop ten candies. For each bottle, you record the height of the eruption created after the candies are dropped into it. 
2. You want to see if fifth-grade boys or fifth-grade girls are faster at solving Ken-Ken puzzles. You randomly select twenty fifth-grade boys and twenty fifth-grade girls from fifth graders in your school district. You time and record how long it takes each student to solve the same Ken-Ken puzzle correctly.