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Statistical Inference Assignment Help


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Point estimation

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  • Concepts of Estimation, Estimators, and Estimates
  • Point estimation
  • Interval estimation
  • Properties of good estimators; unbiasedness
  • Efficiency
  • Consistency
  • Sufficiency
  • Factorization theorem (statement)

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Methods of estimation and interval estimation

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  • Method of moments
  • Method of maximum likelihood
  • Method of minimum variance.
  • Cramer-Rao inequality (statement only)
  • confidence intervals for mean,
  • confidence intervals for variance
  • confidence intervals for proportions

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Small sample tests

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  • Normal tests for mean, (when o known)
  • Normal tests for the difference of means and (when o known)
  • Normal tests for proportion (when o known)
  • t-tests for means (when o unknown),
  • t-tests for the difference of means (when o unknown)
  • paired t-test
  • test for proportion(binomial)
  • chi-square test
  • F-test for the ratio of variances. (derivation not required)
  • Tests for correlation and regression

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Testing of hypotheses, large sample tests

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  • Statistical hypotheses, null and alternative hypotheses:
  • Simple and composite hypotheses,
  • Type-I and type-II errors
  • Critical Region. Size and power of a test, p-value (with problems)
  • Neyman-Pearson approach
  • Large sample tests – z-tests for means
  • z-tests for the difference of means
  • z-tests for proportion
  • z-tests for the difference of proportion
  • Chi-square tests for independence, homogeneity

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Inference for Two Samples

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  • Independent sample design
  • matched pair design
  • pros and cons of each design, side by side box plots
  • comparing means of two populations
  • The large sample confidence interval for the difference of two means
  • large sample test of hypothesis for the difference of two means
  • inference for small samples(confidence intervals and hypothesis test)
  • unequal variance case (confidence intervals and hypothesis tests)
  • sample size determination assuming equal variances
  • confidence intervals and test of hypothesis for matched pair design
  • statistical justification of matched pair design
  • sample size determination for matched pair design
  • comparing the variance of two populations

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Inference for Proportions and Count Data

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  • The large sample confidence interval for the proportion
  • sample size determination for a confidence interval for the proportion
  • large sample hypothesis test on the proportion
  • comparing two proportions in the independent sample design (confidence interval and test of hypothesis)
  • inference for two-way count data (total sample size fixed, row total fixed) the chi-square statistic.

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Statistical Inference Assignment Help