Module 6: Confidence Intervals and Hypothesis Testing

Confidence Interval Definition

a range of values calculated from a sample that is used to estimate where the true population parameter is likely to be.

Point estimate

A single best “guess” (the sample mean/average)

• you literally built the confidence interval around it

Confidence level

The “long-run” success rate of the interval containing the parameter

• is a percentage (e.g. 95%)

• tells us that if we sample/ repeat the process many, many times, 95% of the intervals will contain the true population parameters

Margin of error

The “plus or minus” that follows the point estimate

Confidence Interval Formula

Confidence Interval = Point of Estimate (plus or minus) Margin of Error

Confidence Interval Formula for a Sample Leam

z = critical value from the z-distribution

What are common z-values

Standard Deviation of Samples / STANDARD ERROR FORMULA

Where is the confidence level usually located under a normal distribution graph

• Mainly middle part of graph, the two sides are basically (100% - confidence level) / 2

RStudio Section to Find Z-Value

• whenever we use qnorm, we are finding whatever is in that z value, DOWNWARDS (to the left of the graph)

In what case do we use the t-value/distribution

• when the population SD is unknown

• when sample size is small (x < 30) or large (x > or equal to 30)

T-value/distribution formula for confidence interval

How to find t value (using R)

1. find df (degrees of freedom: sample size - 1)

2. find one of the areas of the normal distribution that the confidence level hasn’t touched

Confidence Interval Formula for a Proportion?

Conditions before using the formula for Confidence Interval for Proportions

• sample must be random

• n x p is (larger than or equal to 5)

• OR n x q (which is 1-p) is (larger than or equal to 5)

Formula for determing how many people (or observations) you need in your sample before actually collecting data

Formula for determing sample size for a proportion (alspo proportion rule - missing or given, whaddya do?)

Rule of 4 (Range Rule of Thumb) to find missing SD for Sample Size formula