Flashcards on Statistics Exam: Time Series and Probability

Statistics Exam: Time Series and Probability Study Guide

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What is the sample variance formula using deviations from the sample mean?

S^2 = (1/(n-1)) * Σ_{i=1}^n (X_i - X̄)^2

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27 cards

Card 1

Question: What is the sample variance formula using deviations from the sample mean?

Answer: S^2 = (1/(n-1)) * Σ_{i=1}^n (X_i - X̄)^2

Card 2

Question: How can sample variance be computed using sums of squares?

Answer: S^2 = (1/(n-1)) * (Σ_{i=1}^n X_i^2 - n X̄^2)

Card 3

Question: How is the sample proportion defined?

Answer: ĤP = X / n (where X is count of successes)

Card 4

Question: What is the approximate (large-sample) 95% confidence interval form for a population mean using Z and sample standard deviation S?

Answer: [X̄ - Z(α/2) * S/√n ; X̄ + Z(α/2) * S/√n]

Card 5

Question: What is the confidence interval for a mean when using the t-distribution?

Answer: [X̄ - t_{n-1}(α/2) * S/√n ; X̄ + t_{n-1}(α/2) * S/√n]

Card 6

Question: How is stratum sample size n_ℓ allocated proportionally from total sample n?

Answer: n_ℓ = (N_ℓ / N) * n

Card 7

Question: What is the large-sample confidence interval for a population proportion ĤP?

Answer: [ĤP - Z(α/2) * √(ĤP(1-ĤP)/n) ; ĤP + Z(α/2) * √(ĤP(1-ĤP)/n)]

Card 8

Question: What is the one-sample Z test statistic for a mean when S is used as the standard error?

Answer: Z = (X̄ - μ_0) / (S / √n) ~ N(0,1)

Card 9

Question: What is the one-sample proportion Z test statistic?

Answer: Z = (ĤP - π_0) / √(π_0(1-π_0)/n) ~ N(0,1)

Card 10

Question: What is the two-sample Z statistic for comparing two means with known/large-sample variance estimates?

Answer: Z = (X̄_1 - X̄_2) / √(S_1^2/n_1 + S_2^2/n_2) ~ N(0,1)