Question

6) 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 mean is about y = 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 results were 32 25 41 35 30 37 29 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 0 = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from u = 28 ml/kg? Use a 0.01 level of significance.

Answer 1

Q.6) Given that, sample size (n) = 7, sample mean $(\bar x)$ = 32.7 ml/kg and population standard deviation $(\sigma)$ = 4.75

The null and alternative hypotheses are,

H0 : μ = 28 ml/kg

Ha : μ ≠ 28 ml/kg

This hypothesis test is a two-tailed test.

Test statistic is,

$Z = \frac {\bar x -\mu}{\frac {\sigma}{\sqrt n }} = \frac {32.7 - 28}{\frac {4.75}{\sqrt 7}} = 2.62$

=> Test statistic = Z = 2.62

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

=> p-value = 2 * [ 1 - P(Z < 2.62) ]

=> p-value = 2 * [ 1 - 0.9956 ]

=> p-value = 2 * 0.0044

=> p-value = 0.0088

Since, p-value is less than 0.01 level of significance, we reject the null hypothesis (H0).

Conclusion : There is sufficient evidence to conclude that Roger's red blood cell volume is different from μ = 28 ml/kg.