Total blood volume (in ml) per body weight (kg) is important in medical research
ID: 3174967 • Letter: T
Question
Total blood volume (in ml) per body weight (kg) is important in medical research. For all healthy adults, the RBC volume is about 28 ml/kg. (Reference: Laboratory and Diagnostic Tests, F. Fischbach). RBC volume that is too low or too high can indicate a medical problem. Suppose that a patient has had seven blood tests and the RBC volumes were: 32 25 41 35 30 37 29. Assume that the variable x (patient's RBC volume) has a normal distribution with sigma = 4.75 ml/kg. Use a 1 % significance level and determine whether the sample data indicate that this patient's RBC volume is different ret healthy adults. Ho: Words: H1: Words: Critical Value Test Value Decision: Conclusion:Explanation / Answer
a. H0: mu=28 (patient's RBC volume is same as that of mean RBC volume of healthy aduluts)
H1:mu=/=28 (patient's RBC volume is different from mean RBC volume of healthy adults)
b. This is a two-tailed test, therefore, critical Z is +-1.96 (note population standard deviation is known, therefore, use 1-sample Z test)
c. For known population standard deviation, and normally distributed population, use 1-sample Z test.
Z=(Xbar-mu)/(sigma/sqrt N), where, Xbar is sample mean and is obtained as, Xbar=sigma X/N, sigma is population standard deviation, and N is sample size.
=(32.71-28)/(4.75/sqrt 7)
=2.63
d. Reject H0, if observed test statistic fall in critical region, that is observed Z>=Critical Z.
e. Conclusion: Here, 2.63>1.96, therefore, reject H0 and conclude that patient's RBC volume is different from mean RBC of healthy adults.