2)A group of 5 patients treated with medicine A weigh 42, 39, 48, 60 and 41Kgs:second group of 7 patient from the same hospital treated with medicine Bweigh 38, 42, 56, 64, 68, 69 and 62Kgs. Do you agree with the claim thatmedicine B increases the weight significantly.11.10. REFERENCE BOOKS1)Agarwal, B.L.‘Basic Statistics’,Wiley Eastern Ltd., New Delhi.2)Chance, W.,‘Statistical methods for Decision’Irwin Inc., Homewood.3)Gopikuttam, G.,‘Quantitative Methods and Operations Research’,HimalayaPublishing House, Bombay.4)Gupta, S.P.,’Statistics Methods’,Sultan Chand and Co., New Delhi5)Levin, R., ‘Statisticsfor Management’,Prentice–Hall of India, New Delhi,1984.11.11. LEARNING ACTIVITIESTen individuals are chosen at random from a population and their heights (ininches) are found to be: 62, 63, 66, 68, 69, 71, 70, 68, 71 and 66. In the light ofthese data, mentioning the null hypothesis, discuss the suggestion that the meanheight in the population is 66 inches.11.12. KEY WORDS1)t-test2)t-test for single mean3)t-test for two mean

102LESSON–12F - TEST12.1. INTRODUCTIONThe main object of F-test is to discover whether the samples have come fromthe same universe. We can get the answer to this problem by the study of Analysisof Variance also called ANOVA, an obvious abbreviated word.12.2. OBJECTIVEThe main aim of this Lesson is to study the Basics of f-test. After goingthrough this Lesson you should be able to understand f-test and ANOVA12.3. CONTENTSF-TestANOVAIllustrationF - testFor testing the difference of more than two samples, the F-test is an alternativeto t-test which can be applied to test the difference of only two or less than twosamples. The test consists of classifying and cross classifying statistical results,and testing the significance of the difference between the samples statistics as wellas among the samples statistics. The analysis of variance is studied by (a) one-wayclassification and (b) two-way classification. If we observe the variation of thevariable with one factor, it is known as one-day classification. If we observe thevariation of the variables with two factors, it is called tow-way classification. Theestimate of population variance which is based on variation between the groups isknown as the mean square between groups. The estimate of population variancethat is based on the variation within group is known as the mean square withingraphs. Since the F-test is based on the ratio of two variances, it is also known asVariance Ratio test. The variance ratio is denoted by F. It is given by:groupsinwithsquareMeangroupsbetweenSquareMeanFIf the calculated value of F is lesser than the table value, all the groups aredrawn from a normal population. To calculate variance ratio, one must determinethe following values:i.The total sum of squaresii.The sum of squares between groupsiii.The sum of squares within groupsIllustration - 1A tea company appoints four salesmen A, B, c and D; and observes their salesin three seasons–

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