204 110.4 F test for two variances

204 110.4 F test for two variances - A B 64.01 63.98 s .326...

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11.4 F TEST FOR THE COMPARISON OF TWO VARIANCES In addition to tests comparing the means or proportions of two populations, there are times when we want to compare the variances of two populations. For example, in selecting between two manufacturing processes we may want to choose the process that is less variable. As a specific example let’s say we want to compare two machines that fill cartons with orange juice. Even though both machines dispense an average of 64 ounces per carton the preferred machine is the one that dispenses more uniformly. Assume two samples are taken where each machine fills 100 cartons; can we state with 99% confidence that machine A is less variable than machine B. Ho: = Ha: α = .01 Machine
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Unformatted text preview: A B 64.01 63.98 s .326 .385 n 100 100 The test used to compare the variances is called the two sample F test in which the F statistic has the following distribution shape. ____________________________________________ If Ho is true we would expect the ratio of F = to be approximately equal to one. (note that the TI calculator and the computer both always have in the numerator). If < , we would expect the ratio to be less than one and if > we would expect the ratio to be greater than one. With the TI we use the 2-SampFTest Input: Data Stats F = .7169 Sx 1 .326 p = .04976 n 1 100 Sx 2 .385 n 2 100 1 : < 2 Thus we cannot state with 99% confidence that machine A is less variable than machine B....
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