A study was conducted at the Virginia-Maryland Regional College of Veterinary Me

Question

A study was conducted at the Virginia-Maryland Regional College of Veterinary Medicine Equine Center to determine if the performance of a certain type of surgery on young horses had any effect on certain kinds of blood cell types in the animal. Fluid samples were taken from each of six foals after surgery. The samples were analyzed for the number of postoperative white blood cell (WBC) leukocytes, and the sample mean was found to be 11.1 units with the sample standard deviation of 0.8 unit. Part a. At 4% level of significance, does the data prove the claim that the mean WBC leukocytes is less than 11 units after surgery? Part b. Now answer using the p-value.

Explanation / Answer

Given that,
population mean(u)=11
sample mean, x =11.1
standard deviation, s =0.8
number (n)=6
null,the mean WBC leukocytes is less than 11 units after surgery Ho: <11
alternate, H1: >11
level of significance, = 0.04
from standard normal table,right tailed t /2 =2.191
since our test is right-tailed
reject Ho, if to > 2.191
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =11.1-11/(0.8/sqrt(6))
to =0.306
| to | =0.306
critical value
the value of |t | with n-1 = 5 d.f is 2.191
we got |to| =0.306 & | t | =2.191
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :right tail - Ha : ( p > 0.3062 ) = 0.3859
hence value of p0.04 < 0.3859,here we do not reject Ho
ANSWERS
---------------
null,the mean WBC leukocytes is less than 11 units after surgery Ho: <11
alternate, H1: >11
test statistic: 0.306
critical value: 2.191
decision: do not reject Ho
p-value: 0.3859
we have evidence that the mean WBC leukocytes is less than 11 units after surgery

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