A study of the health benefits packages for employees of large and small firms w
ID: 3319217 • Letter: A
Question
A study of the health benefits packages for employees of large and small firms was recently completed by Pohman Associates, a management consulting firm. Among the 15 large firms studied, the mean cost of the benefits package was 17.6 percent of salary, with a standard deviation of 2.6 percent. Among the 12 small firms studied, the mean cost of the benefits package was 16.2 percent of salary, with a standard deviation of 3.3 percent. Is there a significant difference between the mean percent of the employees’ salaries spent by large firms and by small firms on health benefits? Use the 0.05 level of significance.
Explanation / Answer
Given that,
mean(x)=17.6
standard deviation , s.d1=2.6
number(n1)=15
y(mean)=16.2
standard deviation, s.d2 =3.3
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.201
since our test is two-tailed
reject Ho, if to < -2.201 OR if to > 2.201
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =17.6-16.2/sqrt((6.76/15)+(10.89/12))
to =1.2013
| to | =1.2013
critical value
the value of |t | with min (n1-1, n2-1) i.e 11 d.f is 2.201
we got |to| = 1.2013 & | t | = 2.201
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.2013 ) = 0.255
hence value of p0.05 < 0.255,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.2013
critical value: -2.201 , 2.201
decision: do not reject Ho
p-value: 0.255
we don't have sufficiant evidence to say that there is a significant difference between the mean percent of the employees’ salaries spent by large firms and by small firms on health benefits
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