Lab 6 Intro: Central Limit Theorem

Goals

Explore the Central Limit Theorem

  • Sampling distribution of \(\bar{x}\), \(\hat{p}\) converges to a bell-shaped and symmetric (normal) distribution as sample size increases.

Counting Bears

Data set 1: counts of polar bears within roughly 3 x 3 km quadrats on Rowley island in northern Foxe Basin, Nunavut.

Picture of a polar bear and Map of Rowley Island.

Figure 1: Left, a photo of a polar bear taken by Seth Stapleton. Right, Rowley Island: bears are indicated by red dots, gray lines show quadrats. Data for today’s lab consist of the number of bears contained within each of 164 quadrats intersecting the island.

Sampling distribution of \(\hat{N}=164\bar{x}\) (a constant times the sample mean)

Estimating proportion of bikers

Proportion of Minneapolis residents that bike to work.

prop(~bike, data=sample(Bike.Y.N, size=50, replace=FALSE), success="Yes")
Picture of a guy biking in the snow.