Question

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 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?

__H₀: μ = 28 ml/kg; H₁: μ < 28 ml/kg; left-tailed

__H₀: μ = 28 ml/kg; H₁: μ > 28 ml/kg; right-tailed    

__H₀: μ = 28 ml/kg; H₁: μ ≠ 28 ml/kg; two-tailed

__H₀: μ ≠ 28 ml/kg; H₁: μ = 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 σ.

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

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

__The Student's t, since we assume that x has a normal distribution with known 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?

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

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

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

__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.

__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.  

Answer 1

Given : Sample size=n=7

Sample mean=

Population standard deviation=

Hypothesized value=

Significance level=

(a) The level of significance is

Hypothesis : ml/kg VS   ml/kg

This is two-tailed test.

(b) The standard normal , Since we assume taht X has a normal distribution with known

The Z value of the sample test statistic is ,

(c) The p-value is ,

p-value=

; From standard normal distribution table

(d) Decision : Here , p-value=0.0052 <

Therefore , reject the null hypothesis .

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

(e) Conclusion :

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.