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Unformatted text preview: MN1025 Business Statistics 24 Lecture 6Friday 15/2/2008 COMPARING THE MEANS OF TWO POPULATIONS Reference: Lind et al. , Chapter 11. Note that they deal with the material in this lecture in a different order. 6.1 Revision: testing the mean In all examples covered last week, the null hypoth esis H was of the form equals something. We looked at three different cases for the alternative hy pothesis, namely less than, greater than and not equal to something. In the following, we will use the Tstatistic and the 5% level of significance. We will assume sample data of size n , mean x and standard deviation s . Less than: Testing H : = 88 against H 1 : < 88. The critical value c is given by P ( T < c ) = 0 . 05. c=1.76 probability density T n=15 0.05 0.1 0.2 0.3 0.442 2 4 Compute T observed = x 88 s/ n . Reject H if T observed < c . The Pvalue is given by P ( T < T observed ). Greater than: Testing H : = 12 against H 1 : > 12. The critical value c is given by P ( T > c ) = 0 . 05, which means P ( T < c ) = 0 . 95. area=0.95 0.05 T probability density n=20 c=1.729 0.1 0.2 0.3 0.442 2 4 Compute T observed = x 12 s/ n . Reject H if T observed > c . The Pvalue is given by P ( T > T observed ). Not equal: Testing H : = 520 against H 1 : negationslash = 520. The critical value c is given by P ( T < c ) + P ( T > c ) = 0 . 05, which means P ( T < c ) = 0 . 975. area=0.95 probability density2.306 2.306 area=0.025 area=0.025 n=9 T 0.1 0.2 0.3 0.442 2 4 Compute T observed = x 520 s/ n . Reject H if T observed < c or T observed > c . The Pvalue is given by P ( T <  T observed  )+ P ( T >  T observed  ). 6.2 Testing for Change We consider first the case where two populations consist of the same objects with two different treat ments, or possibly before and after some treat ment has been applied. The samples will consist of the same objects: they are measured before and after. The question is: has the treatment had any effect? or has it led to an improvement? This is not a new problem; all that we need to do is ap ply last weeks methods to the differences between the populations. Are these differences, on average, zero (that is, no change), or positive (an improve ment), or negative (a worsening)? Examples might be: sales in a particular area before and after a sales campaign, or performance of staff before and after training. 6.3 Example: solutions for seeds Solutions A and B for seeds are tested. The data are for 9 types of seed and give the number of days for growth to 6 inches. Question: is there significant evidence that there is a difference (at the 5% level of significance)? Here we are testing the difference between the times for A and B....
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This note was uploaded on 04/17/2008 for the course MN 1025 taught by Professor Schack during the Spring '08 term at Royal Holloway.
 Spring '08
 SCHACK

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