Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been

Question

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances formula5.mml and formula6.mml give sample variances of s12 = 119 and s22 = 24. (a) Test H0: formula5.mml = formula6.mml versus Ha: formula5.mml formula7.mml formula6.mml with formula8.mml = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.025 = H0:formula5.mml = formula6.mml (b) Test H0: formula5.mml < formula6.mmlversus Ha: formula5.mml > formula6.mml with formula8.mml = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.05 = H0: formula5.mml < formula6.mml

Explanation / Answer

PART A.
Given that,
sample 1
s1^2=119, n1 =9
sample 2
s2^2 =24, n2 =7
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
level of significance, = 0.025
from standard normal table, two tailed f /2 =7.421
since our test is two-tailed
reject Ho, if F o < -7.421 OR if F o > 7.421
we use test statistic fo = s1^1/ s2^2 =119/24 = 4.96
| fo | =4.96
critical value
the value of |f | at los 0.025 with d.f f(n1-1,n2-1)=f(8,6) is 7.421
we got |fo| =4.958 & | f | =7.421
make decision
hence value of |fo | < | f | and here we do not reject Ho
ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
test statistic: 4.96
critical value: -7.421 , 7.421
decision: do not reject Ho

PART B.
| fo | =4.96
critical value
the value of |f | at los 0.05 with d.f f(n1-1,n2-1)=f(8,6) is 4.147
we got |fo| =4.958 & | f | =4.147
make decision
hence value of | fo | > | f | and here we reject Ho
ANSWERS
---------------
null, Ho: ^2 < ^2
alternate, H1: ^2 > ^2
test statistic: 4.96
critical value: 4.147
decision: reject Ho

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