Question

The researchers classified gas turbines into three categories: traditional, advanced, and aeroderivative. Mean heat rate and standard deviation of heat rate for

• Advanced are 9764 and 639
• Aeroderiv are 12312 and 2652
• Traditional are 11544 and 1279

Is there sufficient evidence of a difference between the mean heat rates of traditional turbines and aeroderivative turbines at  alpha =0.05 ? Show all the work

Answer 1

Assume sample sizes for both is 30 because not given in the data
Given that,
mean(x)=11544
standard deviation , s.d1=1279
number(n1)=30
y(mean)=12312
standard deviation, s.d2 =2652
number(n2)=30
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.045
since our test is two-tailed
reject Ho, if to < -2.045 OR if to > 2.045
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =11544-12312/sqrt((1635841/30)+(7033104/30))
to =-1.429
| to | =1.429
critical value
the value of |t α| with min (n1-1, n2-1) i.e 29 d.f is 2.045
we got |to| = 1.42869 & | t α | = 2.045
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.4287 ) = 0.164
hence value of p0.05 < 0.164,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -1.429
critical value: -2.045 , 2.045
decision: do not reject Ho
p-value: 0.164
we do not have enough evidence to support the claim that difference between the mean heat rates of traditional turbines and Aeroderivative turbines