Paper II · 4 Random Variables, Distributions & Inference · TGPSC MPSO / ASO
4.2 Estimation and testing of hypotheses notes
3 notes, in reading order.
- 4.2.1Estimation: point and interval estimation; unbiasedness, consistency, efficiency and sufficiency
Estimation uses a sample statistic to guess an unknown population parameter, either as one value (point estimate) or as a range (confidence interval); a good estimator is unbiased, consistent, efficient and sufficient.
Advanced · 10 min · Full course - 4.2.2Testing of hypotheses: null and alternative hypotheses, errors, level of significance and large sample tests
A test of hypothesis is a rule that uses a sample to reject or not reject a claim (H₀) about a population; for large samples (n ≥ 30) the test statistic Z = (statistic − value under H₀) ÷ standard error is compared with 1.96 / 2.58 (two-tailed) or 1.645 / 2.33 (one-tailed).
Advanced · 9 min · Full course - 4.2.3Small sample tests: Student's t, F and chi-square tests
For small samples (n < 30) from normal populations we use exact tests: t for means (and correlation), F for the ratio of two variances, and χ² for a variance, goodness of fit and independence of attributes, each read from its table with the right degrees of freedom.
Advanced · 9 min · Full course
Practise Estimation and testing of hypotheses. Questions with answers explained, from the same topics.
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