Virtual COMSATS Inferential Statistics Lecture28 Ossam Chohan Assistant

Virtual COMSATS Inferential Statistics Lecture-28 Ossam Chohan Assistant Professor CIIT Abbottabad 1

Recap of previous lectures • Introduction of Correlation and Regression. – Hypothesis testing for correlation and regression coefficients. . 2

Objective of lecture-28 – Practice Problems

Practice Problem-1 • 1000 students at college level were graded according to their IQ level and the economic condition of their parents. • Data is on next slide. • Use the coefficient of contingency to determine the amount of association between economic condition and IQ level. 4

Cont… IQ Level Economic Condition High Low Total Rich 460 140 600 Poor 240 160 400 total 700 300 1000 5

Practice Problem-1 Solution 6

Practice Problem-2 • A movie producer is bringing out a new movie. In order to develop an advertising strategy, he wants to determine whether the movie will appeal most to a particular age group of whether it will appeal equally to all age groups. The producer takes random sample from persons attending the preview of the new movie, and obtain the following results. • What type of the test is suitable in this case • What inference will you draw from this data? 7

Cont… Opinion Age Groups Under 20 20 -39 40 -59 60 and over Total Liked the movie 146 78 48 28 300 Disliked the movie 54 22 42 22 140 Indifferent 20 10 10 20 60 Total 220 110 100 70 500 8

Practice Problem-2 Solution 9

Practice Problem-3 • The campaign manager for a presidential candidate wishes to the test the claim that the proportion of Punjab voters who favor the candidate is at least as large as the proportion of Sindh voters who favor the candidate. Given these data, test the manager’s claim at a 5% level of significance. n Number in favor Punjab 100 36 Sindh 200 84

Practice Problem-3 Solution 11

Practice Problem-4 • A survey of the pocket money received by children in a primary school was made by choosing at random four children of each of the ages 5, 7, 9, 11 years. The amounts of pocket money received are given below: Age (years) Pocket Money (Rs) 5 2 8 10 12 7 9 13 14 16 9 9 14 16 21 11 18 19 23 36

Cont… • Find the regression equation for predicting pocket money from age. • Find the value of r. • Find the coefficient of determination. • Construct 95% CI for regression coefficients α and β. • Test the hypothesis that H 0: β=0

Practice Problem-4 Solution 14

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Practice Problem-5 • In an experiment on reaction times in seconds of two individuals A and B, measured under identical conditions, the following results were obtained: A 0. 41 0. 38 0. 37 0. 42 0. 35 B 0. 32 0. 36 0. 38 0. 33 0. 38 • Test the hypothesis at 0. 05 Level of significance that H 0: δ 2 A=δ 2 B again not equal. • If H 0: δ 2 A=δ 2 B is not rejected in part a, then test the hypothesis at 0. 05 that H 0: μA=μB against not equal.

Practice Problem-5 Solution

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