As the population ages, there is increasing concern about accident-related injur

Question

As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the furthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article:

Carry out a test at significance level 0.10 to see whether the population standard deviations for the two age groups are different (normal probability plots support the necessary normality assumption).
State the relevant hypotheses. (Use 1 for YF and 2 for OF.)

Calculate the test statstics. (Round to two decimal places.)

Explanation / Answer

Given that,
sample 1
s1^2=15.7, n1 =5
sample 2
s2^2 =6.84, n2 =10
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
level of significance, = 0.1
from standard normal table, two tailed f /2 =3.633
since our test is two-tailed
reject Ho, if F o < -3.633 OR if F o > 3.633
we use test statistic fo = s1^1/ s2^2 =15.7/6.84 = 2.3
| fo | =2.3
critical value
the value of |f | at los 0.1 with d.f f(n1-1,n2-1)=f(4,9) is 3.633
we got |fo| =2.295 & | f | =3.633
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: 2.3
critical value: -3.633 , 3.633
decision: do not reject Ho

we dont have evidence to test whether the population standard deviations for the two age groups are different (normal probability plots support the necessary normality assumption).

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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