Stats - Sample distribution Two proportions

How to identify two-proportion problems?

• Mentions (p̂1 - p̂2)

• gives two groups (A and B)

Step 1

State parameters x2

• n = Sample

• pA = p = (population percent 1) “The true proportion/population of people who….”

• pB = (population percent 2) “The true proportion/population of people who….”

• p̂A = “Sample proportion of people…”

• p̂B = “Sample proportion of people…”

“Let (p̂1 - p̂2) = the distance in the proportion of …[repeat (p̂1 - p̂2) but with provided numbers]”

Step 2

Conditions:

2x

• population # multiplied by .1 > given sample population

2x

• np > 10

• n(1-p) > 10

“Since all conditions are met, we can proceed with a normal model.”

Step 3

Find Mean and SD

• Reference two proportion section of the table on formula sheet on page 2 behind page 1.

Step 4

Write:

• P(p̂B > p̂A) = P(p̂A - p̂B < 0)

Find z-score

• use 0 as given number, minus mean over SD.

DRAW NORMAL MODEL—FIND 0 ON MODEL

Step 5

Find normalcdf

• P(p̂A - p̂B < 0) = P(z < [z-score found]) = normalcdf(lower, upper, mean(0), SD(1)).

ACCORDING TO NORMAL DISTRIBUTION….