# 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.30254334323928The 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; two-tailedH0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailed    H0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailedH0: 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 Student's t, since n is large with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since we assume that x has a normal distribution with known σ.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.) 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 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.

Question
2 views

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.

 30 25 43 34 32 39 28

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; two-tailedH0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailed    H0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailedH0: 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 Student's t, since n is large with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since we assume that x has a normal distribution with known σ.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.)

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 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.
check_circle

Step 1

Hey there! Thank you for posting the question. However, since your question has more than 3 subparts, according to our policy, we have solved the first 3 sub parts for you. If you need help with any other part, please re-post the question and mention the part you need help with.

Step 2

a).

The level of significance is 0.01.

Step 3

We will use the two tailed test.

The null and alt...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in