Lecture notes, lecture formula 2 PDF

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Grant MacEwan University STAT 141 Formula Sheet – second midterm Dr. Karen Buro Sampling distributions ¯ • Sampling Distribution of a Sample Mean, X: σ µX¯ = µ, σX¯ = √ n Estimation using a single sample • Confidence Interval for µ (σ known and either population is normal or n is large): σ x¯ ± z ∗ √ n where z ∗ is the (1 − α/2) percentile of the standard normal distribution. • Confidence Interval for µ ( σ unknown and population is normal or n is large): s x¯ ± t∗ √ n where t∗ is the (1 − α/2) percentile of the t-distribution with df = n − 1. • Sample size required to estimate µ within an amount M using a (1−α)×100% confidence interval:  ∗ 2 z σ n≥ M ∗ where z is the (1 − α/2) percentile of the standard normal distribution. Test Statistics using a single sample • One sample Z-test for a mean µ (σ known) z0 =

x¯ − µ0 √ σ/ n...