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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.

33 27 42 36 31 35 29

The sample mean is x ≈ 33.3 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) Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
(b) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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Answer #1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 28

Ha : 28

Test statistic = z

= ( - ) / / n

= (33.3 - 28) / 4.75 / 7

Test statistic = 2.95

P(z > 2.95) = 1 - P(z < 2.95) = 0.0016

P-value = 0.0016

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