9.1
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 μ = 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.
34 25 39 36 31 36 30
The sample mean is x ≈ 33.0 ml/kg. Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and σ = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from μ = 28 ml/kg? Use a 0.01 level of significance.
(a) What is the level of significance?
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.)
a)
H0: = 28
Ha: 28
Level of significance = 0.01
Test statistics
z = - / / sqrt(n)
= 33 - 28 / 4.75 / sqrt(7)
= 2.79
c)
p-value = 2 * P( Z > z)
= 2 * P( Z > 2.79)
= 2 * 0.0026
= 0.0052
Since p-value < 0.05 level, reject H0.
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