AP Stats Test 2

Two-Sample Procedures with means

• The goal of these inference procedures is to compare the responses to two treatments or to compare the characteristics of two populations.

We have INDEPENDENT samples from each treatment or population

We will be interested in the difference of means, so we will use this to find standard error.

Population mean(x-y) = Population mean(x) - population mean(y)

standard deviation(x-y) = √(standard dev x)² + (standard dev y)²

Assumptions:

Mean

• Have two SRS’s from the populations or two randomly assigned treatment groups

• Samples are independent

• Both distributions are approximately normally

  • Have large sample sizes

  • Graph BOTH sets of data

Mean

Since in real-life, we will NOT know both σ’s, we will do t-procedures.

Proportions assumptions

• Two, independent SRS’s from populations ( or randomly assigned treatments)

• Populations at least 10n

• Normal approximation for both

n₂p₂ ≥ 10

n₂(1-p₂) ≥ 10

n₁p₁ ≥ 10

n₁(1-p₁) ≥ 10