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.

34 24 42 33 32 35 29

The sample mean isx32.7ml/kg. Letxbe a random variable that represents Roger's red blood cell volume. Assume thatxhas 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 a0.01 levelof 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?

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

Compute thezvalue of the sample test statistic.

(c) Find (or estimate) theP-value.

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

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

(e) State your conclusion in the context of the application.