Virtual COMSATS Inferential Statistics Lecture32 Ossam Chohan Assistant

Recap of previous lectures • Introduction of Correlation and Regression. – – Simple Regression

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

The Power of a Test • The power of a test with respect to

Special Problem • A random sample of size 4 is drawn from a normal

Course Close-up • • Sample and Sampling? Sampling distribution of different statistics. Why sampling

• Single population, two populations and more than two populations. • Correlation and

References for Course Material and examples • http: //www. isixsigma. com/new-to-sixsigma/getting-started/what-six-sigma/ • http: //www.

• http: //www. utstat. toronto. edu/~olgac/sta 248 _2013/notes/sta 248_Lecture 3. pdf • http:

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Virtual COMSATS Inferential Statistics Lecture-32 Ossam Chohan Assistant Professor CIIT Abbottabad 1

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. 2

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

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 H 0/H 0 is false) • Power = 1 - β 4

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 H 0: µ≤ 30 against H 1: 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. 5

Solution 6

Cont… 7

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 8

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

References for Course Material and examples • http: //www. isixsigma. com/new-to-sixsigma/getting-started/what-six-sigma/ • http: //www. stats. gla. ac. uk/steps/glossary/hy pothesis_testing. html • http: //stattrek. com/estimation-instatistics. aspx • Statistical Theory Part-II by Sher Muhammad Chaudhary. • Statistics for Management by Levin and Rubin. 15

• http: //www. utstat. toronto. edu/~olgac/sta 248 _2013/notes/sta 248_Lecture 3. pdf • http: //www. iienet 2. org/iietrainingcenter/Det ails. aspx? Event. Code=SQC • http: //www. statistics. com/ • Different books for exercise problems. 16