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Virtual COMSATS Inferential Statistics Lecture-32

This lecture provides a recap of previous lectures on correlation and regression, including topics such as simple regression model, hypothesis testing for correlation and regression coefficients, and the power of tests. A special problem is discussed, and concepts like sample and sampling distributions are explained. Various statistical inferences, estimation, hypothesis testing, non-parametric tests, and statistical quality control are covered. Relevant references and resources are provided.

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Virtual COMSATS Inferential Statistics Lecture-32

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  1. Virtual COMSATSInferential StatisticsLecture-32 Ossam Chohan Assistant Professor CIIT Abbottabad

  2. Recap of previous lectures • Introduction of Correlation and Regression. • Simple Regression model. • Hypothesis testing for correlation coefficient. • Hypothesis testing for regression coefficients. • Some practice Problems.

  3. Objective of Lecutre-32 • Power of Test. • Course Close up 

  4. The Power of a Test • The power of a test with respect to the specified alternative hypothesis, is the probability of rejecting a null hypothesis when it is actually false. The power of a test is complement of β. • Recall what is β? • Power = Pr(Reject H0/H0 is false) • Power = 1- β

  5. Special Problem • A random sample of size 4 is drawn from a normal population with known variance 15. A one tailed test of the form H0: µ≤30 against H1: µ > 30 at 5% level of significance is performed. Calculate the probabilities of Type-II error (β) for the values of µ= 31, 32, 34 and 36 in the alternative hypothesis. Also calculate the powers of the test and hence sketch the power curve for this test.

  6. Solution

  7. Cont…

  8. Course Close-up • Sample and Sampling? • Sampling distribution of different statistics. • Why sampling distributions. • Statistical Inferences. • Estimation. • Point and interval estimation. • Hypothesis Testing. • Z, t, chi-square and F-distributions

  9. Single population, two populations and more than two populations. • Correlation and Regression analysis. • Non-Parametric Tests. • Statistical Quality Control.

  10. References for Course Material and examples • http://www.isixsigma.com/new-to-six-sigma/getting-started/what-six-sigma/ • http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html • http://stattrek.com/estimation/estimation-in-statistics.aspx • Statistical Theory Part-II by Sher Muhammad Chaudhary. • Statistics for Management by Levin and Rubin.

  11. http://www.utstat.toronto.edu/~olgac/sta248_2013/notes/sta248_Lecture3.pdfhttp://www.utstat.toronto.edu/~olgac/sta248_2013/notes/sta248_Lecture3.pdf • http://www.iienet2.org/iietrainingcenter/Details.aspx?EventCode=SQC • http://www.statistics.com/ • Different books for exercise problems.

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