Test the hypothesis that, atthe a001 evel of signticance for the given sample da

Question

Test the hypothesis that, atthe a001 evel of signticance for the given sample data Assume that the populaions ane normalty detribted Use the P-value approach Popuation 1 Popuistion 2 24 90 Sute lhe nul andnte hypotheses for his test Use technology to ind the P-value for this test Round to three decimal places as needed) Since the P value i statement regarding the nul hypothesis and draw a concusion for the null hypothesis hee fcent evidence to conclude that the standard devition of Population 1 is significantly greater than the standard deviation of Population 2 at the as 0 01 eve of signficance

Explanation / Answer

Given that,
sample 1
s1^2=166.41, n1 =24
sample 2
s2^2 =81, n2 =16
null, Ho: ^2 = ^2
alternate, H1: ^2 > ^2
level of significance, = 0.01
from standard normal table,right tailed f /2 =3.311
since our test is right-tailed
we use test statistic fo = s1^1/ s2^2 =166.41/81 = 2.054
| fo | =2.054
critical value
the value of |f | at los 0.01 with d.f f(n1-1,n2-1)=f(23,15) is 3.311
we got |fo| =2.054 & | f | =3.311
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: 2.054
critical value: 3.311
decision: do not reject Ho
there is significant evidence to support that standard deviation of population 1 is greater than the standard deviation of population 2 at 0.01 level of significance

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