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 u = 28 ml/kg.t 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 27 43 37 28 35 27 Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and a = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from u = 28 ml/kg? Use a 0.01 level of significance. (a) What is the level of significance? 0.01 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H= 28 ml/kg; H: H< 28 ml/kg; left-tailed O Ho: u* 28 ml/kg; H: u- 28 ml/kg; two-tailed O Ho: H = 28 ml/kg; H: * 28 ml/kg; two-tailed O Ho: H = 28 ml/kg; H: 4> 28 ml/kg; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with unknown a. O The standard normal, since we assume that x has a normal distribution with known a. 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. P-value -2 -1

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