Total blood volume in ml per body weight in kg is important

Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about = 28 ml/kg†. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows.

The sample mean is x 32.9 ml/kg. Let x be a random variable that represents Roger\'s red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Roger\'s red blood cell volume is different (either way) from = 28 ml/kg? Use a 0.01 level of significance.

(a) What is the level of significance?

(b) What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Solution

Set Up Hypothesis
Null Hypothesis H0: U=28
Alternate Hypothesis H1: U!=28
Test Statistic
Population Mean(U)=28
Given That X(Mean)=32.857
Standard Deviation(S.D)=4.75
Number (n)=7
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=32.857-28/(4.75/Sqrt(7)
Zo =2.7054
| Zo | =2.7054
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =2.7054 & | Z | =2.58
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 2.7054 ) = 0.0068
Hence Value of P0.01 > 0.0068, Here we Reject Ho

ANS:
LOS 0.01% is 2.58
Zo =2.71
( P != 2.7054 ) = 0.0068 ~ 0.01