2024-11-17

Overview

  • Intro to Point Estimates w/Data: Chicken Wt vs Feed
  • Math Equation: Sample Mean
  • Plotly Plot: Weights vs Feed
  • Math Equation: Proportion of a Sample
  • GGPlot Histogram: Chick Weights By Feed Type
  • GGPlot Points Plot: Chick Weights By Feed Type
  • R-Code Boxplot and Whiskers: Chick Weights By Feed Type

Chicken Weight vs Feed - Sample Data

  • Point Estimation is the calculation of mean and proportion from a random sample which represents a larger population.

  • Assume we have a random sample of chickens with different diets: Casein, Horsebean, Linseed, Meatmeal, Soybean, Sunflower

  • Here is what the raw data sample from a population of chicks given different feeds looks like:

  weight      feed
1    179 horsebean
2    160 horsebean
3    136 horsebean
4    227 horsebean
5    217 horsebean
6    168 horsebean

Math Equation: Sample Mean

The first important Point Estimate calculation is Sample Mean.

This is expressed as:

Sample Mean = \(\sum x \div n\)



In the following slide, you will see a horizontal line representing the average or mean chick weight: 261.31grams

Chick Weight vs Feed Type

Math Equation: Proportion of a Sample

Another import Point Estimate calculation is Proportion. This is the sample’s number of successes observed (x) divided by the total observations.

It is expressed as:
Sample Proportion = \(x \div n\)


In the previous slide, you saw the number of weights observed above the average (successfully gained weight): 27

The proportion then, of chicks that gained weight from eating is:
Sample Proportion = \(27 \div 71\) = 0.38 or 38% of the sample.


Here are more plots showing the impact on weight of various feed types.

Histogram of Chick Weights By Feed Type

Points Plot of Chick Weights By Feed Type

boxplot(chickwts$weight~chickwts$feed, 
main="Boxplot of Chick Weights By Feed Type",
xlab="Feed Type", ylim=c(0,450), ylab="Chick Weight", 
col=c("blue", "turquoise", "green", "lightgreen",
      "yellow", "lightyellow"))