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. 31 25 43 37 28 39 31 Let x be a random variable that represents Roger's red blood cell volume. Assume that x has 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 a 0.01 level of 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? H0: ? = 28 ml/kg; H1: ? ≠ 28 ml/kg; two-tailedH0: ? = 28 ml/kg; H1: ? < 28 ml/kg; left-tailed H0: ? = 28 ml/kg; H1: ? > 28 ml/kg; right-tailedH0: ? ≠ 28 ml/kg; H1: ? = 28 ml/kg; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?. The Student's t, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with unknown ?. What is the 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Let x be a random variable that represents Roger's red blood cell volume. Assume that x has 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 a 0.01 level of 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?

H₀: ? = 28 ml/kg; H₁: ? ≠ 28 ml/kg; two-tailedH₀: ? = 28 ml/kg; H₁: ? < 28 ml/kg; left-tailed H₀: ? = 28 ml/kg; H₁: ? > 28 ml/kg; right-tailedH₀: ? ≠ 28 ml/kg; H₁: ? = 28 ml/kg; two-tailed

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

The standard normal, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?. The Student's t, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with unknown ?.

What is the 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.

(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 ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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

There is sufficient evidence at the 0.01 level to conclude that Roger's average red cell volume differs from the average for healthy adults.There is insufficient evidence at the 0.01 level to conclude that Roger's average red cell volume differs from the average for healthy adults.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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