Question

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. 32 25 42 37 29 35 30

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 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? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

i.    H0: μ = 28 ml/kg; H1: μ ≠ 28 ml/kg; two-tailed

ii.   H0: μ ≠ 28 ml/kg; H1: μ = 28 ml/kg; two-tailed

iii. H0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailed

iv. H0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

i.   The Student's t, since n is large with unknown σ.

ii. The standard normal, since we assume that x has a normal distribution with known σ.

iii. The standard normal, since we assume that x has a normal distribution with unknown σ.

iv. The Student's t, since we assume that x has a normal distribution with known σ.

**** Compute the z 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.)

**** Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1

from above

i.    H0: μ = 28 ml/kg; H1: μ ≠ 28 ml/kg; two-tailed

b)

ii. The standard normal, since we assume that x has a normal distribution with known σ

z value of the sample test statistic =2.73

P-value =0.0064 ( please try 0.0063 if this comes wrong)