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.

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The sample mean isx≈33.1ml/kg. Letxbe a random variable that represents Roger’s red blood cell volume. Assume thatxhas a normal distribution andσ = 4.75.Do the data indicate that Roger’s red blood cell volume is different (either way) fromμ = 28 ml/kg?Use a0.01 levelof 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; 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

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.

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

The Student’s t, 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.

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.

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