Question

Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the x distribution is about 4.8 (based on information from Diagnostic Tests with Nursing Implications, Springhouse Corporation). Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are 4.9, 4.2, 4.5, 4.1, 4.4, 4.3

(a) Use a calculator to verify that ?̅= 4.40 and ? = 0.28.

(b) Do the given data indicate that the population mean RBC count for this patient is lower than 4.8? Use ? = .05.

(c) Obtain a 90% confidence interval for the mean RBC count.

(d) Can you come to the same conclusion you made in (b) using the interval approach in (c).

Answer 1

Let denotes  the population mean RBC count for this patient.

Conclusion : There is sufficient evidence to support the claim that the population mean RBC count for this patient is lower than 4.8.

c)

Since the upper bound of the confidence interval < 4.8, so we reject the null hypothesis at 90% level of confidence or at 10% level of significance, we can conclude that there is sufficient evidence to support the claim that the population mean RBC count for this patient is lower than 4.8..