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. 34 23 40 37 32 36 30 The sample mean is x = 33.1 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 from μ = 28 ml/kg? Use ? = 0.01. (a) What is the level of significance? State the null hypothesis H0 and the alternate hypothesis H1 . H0 : μ ---Select--- ≥ ≠ = < ≤ > H1 : μ ---Select--- ≥ ≠ < = > ≤ What kind of test is this? two-tailed testleft-tailed test right-tailed test (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is small with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ. Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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.
| 34 | 23 | 40 | 37 | 32 | 36 | 30 |
The sample mean is x = 33.1 ml/kg. Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a
State the null hypothesis
What kind of test is this?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)
(c) Find the P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
(e) State your conclusion.
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