Question

2b) The random samples with sizes 14 = 16 and n2 = 25 respectively were taken from two normal populations. The variances for both samples were s2 = 48 and s= 26 respectively. Using an appropriate hypothesis, carry out a test to determine whether the variance from the first population is higher than the variance from the second population. Use a = 0.05.

Answer 1

2b.

Given that,
sample 1
s1^2=48, n1 =16
sample 2
s2^2 =26, n2 =25
null, Ho: σ^2 = σ^2
alternate, H1: σ^2 > σ^2
level of significance, α = 0.05
from standard normal table,right tailed f α/2 =2.108
since our test is right-tailed
we use test statistic fo = s1^1/ s2^2 =48/26 = 1.85
| fo | =1.85
critical value
the value of |f α| at los 0.05 with d.f f(n1-1,n2-1)=f(15,24) is 2.108
we got |fo| =1.846 & | f α | =2.108
make decision
hence value of |fo | < | f α | and here we do not reject Ho
ANSWERS
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null, Ho: σ^2 = σ^2
alternate, H1: σ^2 > σ^2
test statistic: 1.85
critical value: 2.108
decision: do not reject Ho
we do not have enough evidence to support the claim that first variance for the first population  is higher than second variance for second population.