Business Statistics and Quantitative Methods
This domain tests descriptive statistics, probability, sampling, estimation, hypothesis testing, regression and quantitative decision tools.
Core rules
- Central tendency: mean sensitive to outliers; median robust; mode most frequent. Standard deviation measures spread around the mean.
- Probability: addition rule P(A∪B) = P(A) + P(B) − P(A∩B); multiplication for independent events P(A∩B) = P(A)P(B).
- Normal distribution: 68% within 1 SD, 95% within 1.96 SD, 99.7% within 3 SD.
- Sampling distribution: standard error of mean = σ/√n. Central limit theorem: sample means approach normality as n grows.
- 95% confidence interval for mean = x̄ ± 1.96 × SE (large sample).
- Hypothesis testing: H0 vs H1; α = P(Type I error); β = P(Type II error); p-value is the probability of data at least as extreme as observed, assuming H0 true. Reject H0 if p < α.
- Regression: R² is the proportion of variance explained; correlation does not prove causation.
Worked example. Sample mean 50, SD 10, n = 100. SE = 10/10 = 1. 95% CI = 50 ± 1.96 = [48.04, 51.96]. Testing H0: μ = 48, z = (50 − 48)/1 = 2.00; since |2.00| > 1.96, reject H0 at 5% (two-tailed).
Traps. SE is not SD. A p-value is not the probability that H0 is true. Type I error is rejecting a true H0. One-tailed and two-tailed critical values differ. High R² does not prove causality.