Methods - Chapter 10

Interval Estimate

point estimate +/- margin of error, provides information about how close the point estimate is to the parameter.

Margin of Error

computed with σ or s. σ is a better estimate than s.

σ Known

when σ is known or can be solved for. Use z-value in the margin of error.

σ Known Interval Estimate of μ

x̄ ± z_α/2*(σ/√n)

Margin of Error Calculation

ME = z_α/2*(σ/√n)

Values of z_α/2 for Commonly Used Confidence Levels

90% = 1.645, 95% = 1.960, 99% = 2.576

Confidence Level

1 - α; the level that we are ##% confident that the interval estimate includes μ.

Confidence Coefficient

confidence level percentage turned into a number.

Normal Distribution Approximation

if n ≥ 30, it's adequate. If population dist. highly skewed/has outliers, n ≥ 50. If population only roughly symmetric/believed to be at least approximately normal, n ≤ 15

E

desired margin of error, often a smaller amount than ME because it guarantees better accuracy. To reach this, increase n.

Necessary Sample Size

n = (z_α/2²*σ²)/E²