You want to know whether the population variances in the salaries of seniors and

Question

You want to know whether the population variances in the salaries of seniors and managers of public accounting firms are equal. To know this, you collect a sample of 25 seniors and obtain the sample variance of 2.1. You also collect another sample of 26 managers and obtain the sample variance of 11.1. The salary data were provided in thousands of dollars. At a .05 level of significance, what is your conclusion? What is the appropriate null hypothesis in this problem? a. H_0: sigma^2 senior lessthanorequalto sigma^2 manager b. H_0: sigma^2 manager lessthanorequalto sigma^2 senior c. H_0: sigma^2 senior = sigma^2 manager

Explanation / Answer

Given that,
sample 1
s1^2=11.1, n1 =26
sample 2
s2^2 =2.1, n2 =25
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
level of significance, = 0.05
from standard normal table, two tailed f /2 =2.257
since our test is two-tailed
reject Ho, if F o < -2.257 OR if F o > 2.257
we use test statistic fo = s1^1/ s2^2 =11.1/2.1 = 5.29
| fo | =5.29
critical value
the value of |f | at los 0.05 with d.f f(n1-1,n2-1)=f(25,24) is 2.257
we got |fo| =5.286 & | f | =2.257
make decision
hence value of | fo | > | f | and here we reject Ho
ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
test statistic: 5.29
critical value: -2.257 , 2.257
decision: reject Ho

we don't have evidence that it is equal

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.