PT SET 2 — Word Problems & Application

Individual Z problem

z = x − μ / σ

Individual Z interpretation

Positive z = above μ, negative z = below μ, z > 2 = generally unusual

Sample mean Z problem

z = x̄ − μ / (σ / √n)

Sampling distribution problem

ux̄ = μ and SE = σ / √n

CLT problem

If n ≥ 30 treat the sampling distribution of x̄ as approximately normal

Confidence interval problem P.Z.CV.CI.

Identify the parameter, then choose Z T or proportion, then find critical value and E, then build the interval

Known σ mean problem

use Z

Unknown σ mean problem

use T and df = n − 1

Proportion problem —> P, Z

successes x and n → calculate p̂ = x / n —> then use a proportion Z interval

Plus 4 problem

Given x and n → p̃ = x + 2 / n + 4

Find interval from estimate and E Estimate 50 and E 3 → interval

47 to 53

Find E from interval Interval 40 to 50 → E

5

Find estimate from interval Interval 40 to 50 → estimate =

45

Find width from E, E = 5 → width =

10

Confidence comparison: 99 percent confidence is X than 95 percent confidence with the same data

99 percent confidence is wider than 95 percent confidence with the same data

Sample size comparison: Larger n → ? E → ? interval

Larger n → smaller E → narrower interval

Standard deviation comparison: Larger σ or s → ? E → ? interval

Larger σ or s → larger E → wider interval

Asked how many observations are needed for a mean → use ? formula

mean sample size

Asked how many people or successes are needed → use ? formula

proportion sample size

No prior proportion problem: No prior p̂ → use ?

0.50

Sample size calculation

Calculate n then always round UP

Degrees of freedom problem: n = 20 → df =

19

Confidence level problem: 95 percent → α = 0.05 → α/2 =

0.025

Confidence level problem: 99 percent → α = 0.01 → α divided by 2 =

0.005

Confidence level problem: 90 percent → α = 0.10 → α divided by 2 =

0.05

Method recognition: σ known → ?; σ unknown or s given → ?; proportion → ?

σ known → Z; σ unknown or s given → T; proportion → Z

Formula recognition

Identify what the problem asks for before choosing the formula