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7. Parametric test - F test example ( Enter your problem )
  1. Example-1
  2. Example-2
Other related methods
  1. Non parametric test - Sign test
  2. Non parametric test - Mann whitney U test
  3. Non parametric test - Kruskal-wallis test
  4. Non parametric test - Chi square test
  5. Non parametric test - Median test
  6. Non parametric test - Mood's Median test
  7. Parametric test - F test
  8. Parametric test - t-test
  9. Parametric test - Standard error

6. Non parametric test - Mood's Median test
(Previous method)
2. Example-2
(Next example)

1. Example-1





1. Parametric test - F test for the following data
19,22,24,27,24,18,20,19,25
26,37,40,35,30,30,40,26,30,35,45, Significance Level `alpha=0.05` and One-tailed test


Solution:
Step-1: Let us take the hypothesis that the two sample have same variance
Null Hypothesis `H_0 : S_1^2 = S_2^2`

Alternative Hypothesis `H_1 : S_1^2 != S_2^2`

Step-2: Calculate `S_1^2` and `S_2^2`

`bar x_1=22` and Variance `S_(1)^2=10` for `19,22,24,27,24,18,20,19,25`


`x``x - bar x = x - 22``(x - bar x)^2`
19-39
2200
2424
27525
2424
18-416
20-24
19-39
2539
---------
`sum x=198``sum (x - bar x)=0``sum (x - bar x)^2=80`


Mean `bar x = (sum x)/n`

`=(19 + 22 + 24 + 27 + 24 + 18 + 20 + 19 + 25)/9`

`=198/9`

`=22`



Sample Variance `S^2 = (sum (x - bar x)^2)/(n-1)`

`=80/8`

`=10`



`bar x_2=34` and Variance `S_(2)^2=38` for `26,37,40,35,30,30,40,26,30,35,45`


`x``x - bar x = x - 34``(x - bar x)^2`
26-864
3739
40636
3511
30-416
30-416
40636
26-864
30-416
3511
4511121
---------
`sum x=374``sum (x - bar x)=0``sum (x - bar x)^2=380`


Mean `bar x = (sum x)/n`

`=(26 + 37 + 40 + 35 + 30 + 30 + 40 + 26 + 30 + 35 + 45)/11`

`=374/11`

`=34`



Sample Variance `S^2 = (sum (x - bar x)^2)/(n-1)`

`=380/10`

`=38`



Step-3:
`F=("Larger estimate of variance")/("Smaller estimate of variance")`

`=38/10`

`=3.8`

Step-4:
`df_1=8,df_2=10,F_(0.05)=3.0717`

As calculated `F=3.8 > 3.0717`

So, `H_0` is rejected.


This material is intended as a summary. Use your textbook for detail explanation.
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6. Non parametric test - Mood's Median test
(Previous method)
2. Example-2
(Next example)





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