Question

For the following experiment, you will use the dataset BodyFat in the Sweeney Stats Group. Bodyfat was collected from a group of 252 CrossFit athletes. The average bodyfat for the American population is 23.4. Test the conclusion that the average bodyfat for Crossfit Athletes is less than the average bodyfat for the American population. Test using = .05. In addition to running the hypothesis test, answer the following question: Would you use this data to claim that CrossFit Athletes are in better shape than Americans? (Remember, lower body fat is better.)

Answer 1

Assumed data,because not given in the data
sample mean, x =22
standard deviation, s =6
Given that,
population mean(u)=23.4

number (n)=252
null, Ho: μ=23.4
alternate, H1: μ<23.4
level of significance, α = 0.05
from standard normal table,left tailed t α/2 =1.651
since our test is left-tailed
reject Ho, if to < -1.651
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =22-23.4/(6/sqrt(252))
to =-3.7041
| to | =3.7041
critical value
the value of |t α| with n-1 = 251 d.f is 1.651
we got |to| =3.7041 & | t α | =1.651
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -3.7041 ) = 0.00013
hence value of p0.05 > 0.00013,here we reject Ho
ANSWERS
---------------
null, Ho: μ=23.4
alternate, H1: μ<23.4
test statistic: -3.7041
critical value: -1.651
decision: reject Ho
p-value: 0.00013
we have enough evidence to support the claim that the average bodyfat for Crossfit Athletes is less than the average bodyfat for the American population.