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 (see reference). Suppose that Roger has had seven blood tests, and the red blood cell volumes were:
32 25 41 35 30 37 29
The sample mean is  ≈ 32.7 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.
Please provide the following information:
(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?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.