Question

In: Statistics and Probability

Total blood volume (in ml) per body weight (in kg) is important in medical research. For...

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 43 33 29 36 31

The sample mean is 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 σ = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from μ = 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?

a. H0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailed

b. H0: μ = 28 ml/kg; H1: μ ≠ 28 ml/kg; two-tailed    

c. H0: μ ≠ 28 ml/kg; H1: μ = 28 ml/kg; two-tailed

d. H0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailed


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

a. The standard normal, since we assume that x has a normal distribution with known σ.

b. The Student's t, since n is large with unknown σ.

c. The Student's t, since we assume that x has a normal distribution with known σ.

d. The standard normal, since we assume that x has a normal distribution with unknown σ.


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.)

(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 α?

a. At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

b. At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

c. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

d. At the α = 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.

a. 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.

b. 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.

Solutions

Expert Solution

a) The level of significance is 0.01.

Option - b) H0: = 28 ; H1: 28; two - tailed

b) Option - a) The standard normal, since we assume that x has a normal distribution with known .

The test statistic z = ()/()

                               = (32.7 - 28)/(4.75/)

                               = 2.62

c) P-value = 2 * P(Z > 2.62)

                 = 2 * (1 - P(Z < 2.62))

                 = 2 * (1 - 0.9956)

                 = 0.0088

d) Since the P-value is less than the significance level(0.0088 < 0.01), so we should reject the null hypothesis.

Option - a) At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

e) Option - a) 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.

     


Related Solutions

Total blood volume (in ml) per body weight (in kg) is important in medical research. For...
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. 31 25 41 37 31 37 29 The sample mean is x ≈ 33.0 ml/kg. Let x...
Medical: Red Blood Cell Volume Total blood volume (in ml) per body weight (in kg) is...
Medical: Red Blood Cell Volume 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 m 5 28 ml/kg (Reference: Laboratory and Diagnostic Tests by F. Fischbach). Red blood cell volume that is too low or too high can indicate a medical problem (see reference). Suppose that Roger has had seven blood tests, and the red blood cell volumes were 32 25 41 35...
The human body has a blood volume of about 5 liters (p = 1060 kg /...
The human body has a blood volume of about 5 liters (p = 1060 kg / m3). The total volume of blood with a cell density of 1225 kg / m3 turned out to contain 1% white blood cells and 44% red blood cells. Red blood cells 7.5 x 106 m in diameter. Determine the total number of blood cells in human blood
An intramuscular medication is given at 3.00mg per kg body weight. If the patient weighs 157...
An intramuscular medication is given at 3.00mg per kg body weight. If the patient weighs 157 pounds, how much medication is needed? Show work
Total plasma volume is important in determining the required plasma component in blood replacement therapy for...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 8.00 ml/kg for the distribution of blood plasma. (a) Find a...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.20 ml/kg for the distribution of blood plasma. (a) Find a...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 41male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 8.00 ml/kg for the distribution of blood plasma. (a) Find a 99%...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 41male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 8.00 ml/kg for the distribution of blood plasma. (a) Find a 99%...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.20 ml/kg for the distribution of blood plasma. (a) Find a...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for...
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.60 ml/kg for the distribution of blood plasma. (a) Find a...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT