AP STATS: WARM-UP

1. AP STATS: WARM-UP Ms. Phipps has employed a team of statisticians to determine whether the student body and faculty enjoy the new SAGE lunches at MB compared to last year. In addition, they want to determine which particular lunches and foods the students and faculty and enjoy most. How could you go about determining this information? Be Specific. Discuss this question with your partner and take 5 minutes to create a semi-detailed plan to present to the mayor.

2. Sampling and why it matters? Polls, ratings, and experiments. Time and cost typically prevent us from polling the entire population (the group that we want information about). So instead, we oftentimes rely on samples to help us determine estimates of what would happen had we been surveying the entire population. Say we want to know the number of minutes that Moses Brown HS students spend on average per school night completing homework? Perhaps economists want to determine the unemployment rate? Or a network wants to determine TV ratings. We could ask every person (the population) or we could take a sample? How do we choose a SAMPLE that truly represents ALL Moses Brown HS students, or All Providence residents, or all U.S. citizens? This section is all about statistical designs for choosing samples.

3. A REMINDER: Observational Study versus an Experiment • In an observational study: we observe individuals and measure variables of interest BUT DO NOT ATTEMPT TO INFLUENCE THE RESPONSES. • EXPERIMENT: WE DELIBIRATELY IMPOSE SOME TREATMENT ON INDIVIDUALS IN ORDER TO OBSERVE THEIR RESPONSES. • Think of lung cancer and smoking.

4. Sampling Vs. a Census • Sampling: Study a part in order to gain information about the whole. • Census: attempts to contact every individual in the population.

5. SAMPLING METHODS Voluntary Response Sample: consists of people responding to a general appeal. It is BIASED (i.e. it systematically favors certain outcomes) because people with strong opinions (esp. negative ones) are likely to respond. Example: call-in to give your answer, please help me with my stat project (survey monkey). Convenience Sampling: Choosing individuals who are easiest to reach. (IT IS BIASED AS WELL) Example: Mall interviewing – interviewers are examining a non-representative sample and might choose people to ask selectively. UNBIASED: a statistics is unbiased if the mean of the sampling distribution equals the mean of the population (we will discuss this later on).

6. Representative Sampling The simplest way to use chance to select a sample is to place names in a hat (the population) and draw out a handful (a sample). Simple Random Sample (SRS): every individual in the population has an equal chance of being selected. AVOIDS BIAS

7. Choosing an SRS using random digits Software programs can “draw the names out of a hat” for you. If you don’t have software, use a table of values: Step 1: LABEL – assign a numerical value to each population member Step 2: Table: Use Table B to select labels at random. Step 3: Stopping Rule: Stop when you choose your sample Step 4: Identify the sample. MATH – PRB – RandINT(1,30)

8. Probability Sample • When the sample is chosen by chance (like an SRS). • Stratified Random Sample: first divide the population into groups of individuals, called strata, that are similar in some way that is important to response. Then choose a separate SRS in each stratum and combine these SRS’s to form a full sample. • STRATA can be geographic, racial, rural/metropolitan, etc.

9. Cluster Sampling Cluster sampling divides the population into groups, or clusters. Some of these clusters are randomly selected. Then ALL individuals in the cluster are selected to be in the sample. EXAMPLE: sampling students about whether they think there is enough time on the free response section of the AP Stats exam. Pick a school at random, than survey everyone at the school. EASIER TO DO…

10. Multistage Sampling Design • Combine different elements. • Stratify, cluster, SRS