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# F Test

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### F Test

1. 1. F-test Variance ratio test
2. 2. F-test-Variance ratio test <ul><li>The test based on the test statistic which follows F-distribution is called F- test </li></ul>
3. 3. Significant difference between variances of two populations based on small samples drawn from those populations <ul><li>s 1 ²n 1 </li></ul>n 1 -1 s 2 ²n 2 n 2 -1 F =
4. 4. <ul><li>In the F-ratio we always take the larger of the two estimates in the numerator and smaller in the denominator </li></ul><ul><li>The degree of freedom is (n 1 -1) and (n 2 -1) </li></ul>
5. 5. Assumptions <ul><li>Samples are drawn at random </li></ul><ul><li>Samples are drawn from normal populations </li></ul><ul><li>Population standard deviations are treated as equal but unknown </li></ul>
6. 6. uses <ul><li>Test equality of variances of two populations </li></ul><ul><li>To test equality of means of three or more populations (known as analysis of variance) </li></ul>
7. 7. Question no 1 <ul><li>The standard deviation of two samples of sizes 10 and 14 from two normal populations are 3.5 and 3.0 respectively.Examine whether the standard deviations of the populations are equal. </li></ul>
8. 8. Question no 2 <ul><li>Two samples are drawn from two normal populations . From the following data test whether the two samples have the same variance at 5%level </li></ul>
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