Course Contents
Random sampling, sampling distribution of sample mean & difference between two sample means. Sampling distribution of S^2, t-distribution, F-distribution.
Problems of estimation, estimator and estimate, point and interval estimation, properties of estimator, unbiasedness, consistency, efficiency and sufficiency. Methods of estimation: moment and maximum likelihood with simple examples. Confidence interval and its interpretation, large sample confidence intervals for mean and difference between two means, proportion and difference between two proportions, one sided confidence intervals.
Statistical hypothesis, null and alternative hypothesis, simple and composite hypothesis. Type-I and type-II errors, one-sided and two-sided tests. Concept of power of a test, OC curve, level of significance, determination of sample size, large and small sample test of hypothesis for mean and difference between two means, proportion and difference between two proportions. Confidence interval for single variance, Chi Square test for single variance, F-test for variance ratio. Chi square test for goodness of fit of proportions (multinomial distribution), Binomial, Poisson and Normal distributions. Contingency tables, Test of Association / Independence. Yates correction for continuity, Co-efficient of contingency.
Case Study:
Analyze the real data and present the work in the form of report.
Course Synopsis
Introduction to sampling distributions, methods of estimation and testing of hypothesis.
Course Learning Outcomes
At the end of the course, the student has basic theoretical knowledge about fundamental principles for statistical inference. The student has knowledge about Sampling distribution of mean and difference between two sample means, Sampling distribution of , t-distribution and F-distribution. The student can perform point estimation, interval estimation and hypothesis testing. Further, the student can evaluate the properties of these estimators. The students has the knowledge to perform chi square goodness of fit test of proportions, binomial, Poisson and normal distributions. The students can also test the independence of two variables.
The Sampling Distribution of the Difference in Sample Means (X_1 bar - X_2 bar) by jbstatistics
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Sampling Distributions: Difference Between Means by onlinestatbook
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Introduction to the t Distribution (non-technical) by jbstatistics
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What is the t-distribution? An extensive guide! by zedstatistics
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An Introduction to the Chi-Square Distribution by jbstatistics
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What is the Chi-Squared distribution? Extensive video! by zedstatistics
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An Introduction to the F Distribution by jbstatistics
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Estimation by AtewS Online Study
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Estimation of Parameters by MonSer7605006
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THEORY OF ESTIMATION STATISTICS ISI MSTAT,IIT JAM,ISS,MSC STATISTICS IAS STATISTICS OPTIONAL by SOURAV SIR'S CLASSES
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Method of Moments Estimation by math et al
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Maximum Likelihood Examples by math et al
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Simple Random Samples by R Backman
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The Sampling Distribution of the Sample Mean by jbstatistics
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The Sampling Distribution of the Sample Mean by jbstatistics
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Properties of Good Estimator by Hai Liang Neoh
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Confidence Intervals - Introduction by Joshua Emmanuel
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98% Confidence Interval for a Population Mean (Sigma Unknown) - Part 1 by Maths and Stats
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98% Confidence Interval for a Population Mean (Sigma Unknown) - Part 2 by Maths and Stats
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Confidence interval of difference of means (known pop. Variances) by Khan Academy
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Independent Two-Sample Confidence Interval for the Difference Between Two Means (small sample sizes) by STA 270: Applied Statistics
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Large Sample Confidence Interval for a Population Proportion by STA 270: Applied Statistics
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Confidence Interval for the Difference Between Proportions by Steve Mays
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The Sampling Distribution of the Sample Variance by jbstatistics
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Proof that the Sample Variance is an Unbiased Estimator of the Population Variance by jbstatistics
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An Introduction to the Chi-Square Distribution by jbstatistics
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What is the Chi-Squared distribution? Extensive video! by zedstatistics
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An Introduction to the F Distribution by jbstatistics
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Type 1 and Type 2 errors - Statistics Help by Dr Nic's Maths and Stats
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lecture- 27 || Type one error & type two error by Meta Education
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Hypothesis Testing| Core Concepts by Six Sigma Pro SMART
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Hypothesis testing. Null vs alternative by 365 Data Science
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Book Title : Probability and Statistics for Engineers & Scientists
Author : Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye
Edition : Eighth Edition
Publisher : Prentice Hall, Inc. New York
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Title : Hypothesis Testing
Type : Presentation
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Title : Chi Square
Type : Presentation
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Title : Estimation
Type : Presentation
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Title : Statistical Inference
Type : Presentation
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Title : Sampling dist. of sample mean
Type : Presentation
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Title : sampling distribution
Type : Presentation
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Title : Hypothesis Testing
Type : Presentation
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