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	-3	9
22	0	0
24	2	4
27	5	25
24	2	4
18	-4	16
20	-2	4
19	-3	9
25	3	9
---	---	---
`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	-8	64
37	3	9
40	6	36
35	1	1
30	-4	16
30	-4	16
40	6	36
26	-8	64
30	-4	16
35	1	1
45	11	121
---	---	---
`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.