Statistics

Cards (10)

• 1
  Front

  What is the formula for the sample mean?

  Back

  x̄ = (Σxᵢ) / n, where xᵢ are individual values and n is the sample size.

• 2
  Front

  What is the formula for sample variance?

  Back

  s² = Σ(xᵢ - x̄)² / (n - 1), using n - 1 (Bessel's correction) to produce an unbiased estimate of population variance.

• 3
  Front

  What are the parameters that fully define a normal distribution?

  Back

  The mean (μ), which determines the center, and the standard deviation (σ), which determines the spread. Written as N(μ, σ²).

• 4
  Front

  What is the formula for a z-score?

  Back

  z = (x - μ) / σ, representing how many standard deviations a value x is from the mean μ.

• 5
  Front

  What does the Central Limit Theorem state?

  Back

  For a sufficiently large sample size n, the sampling distribution of the sample mean approaches a normal distribution with mean μ and standard error σ/√n, regardless of the population's distribution.

• 6
  Front

  What is the formula for a 95% confidence interval for a population mean?

  Back

  CI = x̄ ± 1.96 × (σ/√n) when σ is known, or x̄ ± t*(s/√n) when using the sample standard deviation s with a t-distribution.

• 7
  Front

  In hypothesis testing, what is the difference between a Type I and a Type II error?

  Back

  A Type I error is rejecting a true null hypothesis (false positive); its probability equals α. A Type II error is failing to reject a false null hypothesis (false negative); its probability is β.

• 8
  Front

  What is the formula for a z-test statistic when testing a population mean?

  Back

  z = (x̄ - μ₀) / (σ/√n), where μ₀ is the hypothesized population mean and σ/√n is the standard error.

• 9
  Front

  What does the coefficient of determination (R²) measure in regression?

  Back

  R² measures the proportion of variance in the dependent variable explained by the independent variable(s). It ranges from 0 to 1, with 1 indicating a perfect fit.

• 10
  Front

  What is the least-squares regression line formula?

  Back

  ŷ = b₀ + b₁x, where b₁ = Σ(xᵢ - x̄)(yᵢ - ȳ) / Σ(xᵢ - x̄)² is the slope and b₀ = ȳ - b₁x̄ is the y-intercept.