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###### 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.

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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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