Question: Medical: Red Blood Cell volume Total blood volume ( in ml) per body weight ( in kg) is important in medical research, For healthy adult , the red blood cell volume mean is about u = 28 ml/kg. Red blood cell volume 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

32 25 41 35 30 37 29

The sample mean is \(\bar{X}\) = 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 \(\sigma \) = 4.75. Do the data indicate that Roger’s red blood cell volume is different (either way) from \(\mu \) = 28 ml/kg? Use a 0.01 level of significance.

1. What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right tailed, or two tailed test?
2. What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistic?
3. Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P- value.
4. 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 \(\alpha \) ?
5. State your conclusion in the context of the application.

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