Question

Obtain or compute the following quantities.

(a) F0.05, 4, 7 (Round your answer to two decimal places.)
(b) F0.05, 7, 4 (Round your answer to two decimal places.)
(c) F0.95, 4, 7 (Round your answer to three decimal places.)
(d) F0.95, 7, 4 (Round your answer to three decimal places.)
(e) the 99th percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to two decimal places.)
(f) the 1st percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to three decimal places.)
(g) P(F ≤ 6.26) for v1 = 5, v2 = 4 (Round your answer to two decimal places.)
(h) P(0.177 ≤ F ≤ 4.74) for v1 = 10, v2 = 5 (Round your answer to two decimal places.)

Answer 1

a)

b)

c)

d)

e)

f)

g)

h)

Explanation:

Answer 2

a)
`F_(0.05,4,7)=0.16`

b)
`F_(0.05,7,4)=0.24`

c)
`F_(0.95,4,7)=4.12`

d)
`F_(0.95,7,4)=6.09`

e)
`F_(0.99,8,12)=4.50`

f)
`F_(0.01,8,12)=0.18`

g)
`P(F_(5,4) \leq 6.26)=0.95`

h)
`P(0.177 \leq F_(10,5) \leq 4.74)=0.94`

Explanation:

(a) F0.05, 4, 7 (Round your answer to two decimal places.)

For this case we need a valueof the F distribution with 4 degrees of freedom for the numerator and 7 for the denominator that accumulates 0.05 of the area on the left tail. We can use the following excel code: "=F.INV(0.05,4,7)". And we got:

`F_(0.05,4,7)=0.16`

(b) F0.05, 7, 4 (Round your answer to two decimal places.)

For this case we need a valueof the F distribution with 7 degrees of freedom for the numerator and 4 for the denominator that accumulates 0.05 of the area on the left tail. We can use the following excel code: "=F.INV(0.05,7,4)". And we got:

`F_(0.05,7,4)=0.24`

(c) F0.95, 4, 7 (Round your answer to three decimal places.)

For this case we need a valueof the F distribution with 4 degrees of freedom for the numerator and 7 for the denominator that accumulates 0.95 of the area on the left tail. We can use the following excel code: "=F.INV(0.95,4,7)". And we got:

`F_(0.95,4,7)=4.12`

(d) F0.95, 7, 4 (Round your answer to three decimal places.)

For this case we need a valueof the F distribution with 7 degrees of freedom for the numerator and 4 for the denominator that accumulates 0.95 of the area on the left tail. We can use the following excel code: "=F.INV(0.95,7,4)". And we got:

`F_(0.95,7,4)=6.09`

(e) the 99th percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to two decimal places.)

So for this case we need a value on the F distribution with 8 degrees of freedom for the numerator and 12 for the denominator that accumulates 0.99 of the area on the left tail. And we can use the following excel code: "=F.INV(0.99,8,12)". And we got:

`F_(0.99,8,12)=4.50`

(f) the 1st percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to three decimal places.)

So for this case we need a value on the F distribution with 8 degrees of freedom for the numerator and 12 for the denominator that accumulates 0.01 of the area on the left tail. And we can use the following excel code: "=F.INV(0.01,8,12)". And we got:

`F_(0.01,8,12)=0.18`

(g) P(F ≤ 6.26) for v1 = 5, v2 = 4 (Round your answer to two decimal places.)

For this case we want to find the probability that the F distribution with 5 degrees on the numerator and 4 on the denominator would be less or equal than 6.26. We can use the following excel code: "=F.DIST(6.26,5,4,TRUE)". And we got

`P(F_(5,4) \leq 6.26)=0.95`

(h) P(0.177 ≤ F ≤ 4.74) for v1 = 10, v2 = 5 (Round your answer to two decimal places.)

For this case we want to find the probability that the F distribution with 10 degrees on the numerator and 5 on the denominator would be between 0.177 and 4.74. We can use the following excel code: "=F.DIST(4.74,10,5,TRUE)-F.DIST(0.177,10,5,TRUE)". And we got

`P(0.177 \leq F_(10,5) \leq 4.74)=0.94`