class: center, middle ### Sampling Distributions and Estimation <img src="img/DAW.png" width="450px"/> <span style="color: #91204D;"> .large[Kelly McConville | Math 141 | Week 7 | Fall 2020] </span> --- ## Announcements/Reminders * Exam this week. + No Week 7 labs (Th, Oct 15h or Fri, Oct 16th). + No Class on Fri, October 16th. + [Sign up for your 10 minute oral exam](https://docs.google.com/spreadsheets/d/18abmsFaa1JhwLZUbqgKZ0y7gOBH1M8brLln_TjyOspo/edit?usp=sharing) + You must do the 2 hour takehome exam BEFORE your oral exam! * Lab 6 will definitely help with studying for the exam! --- ## Week 7 Topics * **Sampling Distributions** * Estimation * Election Forecasting --- ## Goals for Today * Study properties of Sampling Distributions. * Practice generating Sampling Distributions in R. --- ## Sampling Distribution of a Statistic Steps to Construct an (Approximate) Sampling Distribution: 1. Decide on a sample size, `\(n\)`. -- 2. Randomly select a sample of size `\(n\)` from the population. -- 3. Compute the sample statistic. -- 4. Put the sample back in. -- 5. Repeat Steps 2 - 4 many (1000+) times. --- ## Sampling Distribution of a Statistic <img src="img/samp_dist.png" width="65%" style="display: block; margin: auto;" /> * Center? * Spread? + Standard error = standard deviation of the statistic * Shape? -- **What happens to the center/spread/shape as we increase the sample size?** -- **What happens to the center/spread/shape if the true parameter changes?** --- class: inverse, center, middle ### Let's practice with the samplingDistributions.Rmd handout.