Question

Near the city of Lima in Peru, there is an extremely poor indigenous population. The volunteer doctors who help these people suspect that this population suffers from diseases caused by leukopenia (Decreased white blood cells). The last 10 patients showed white blood cell levels of 4.64, 4.34, 5.32, 4.99, 3.98, 4.53. 4.82, 6.29, 4.35 and 4.12 (mm^8).

1. If historical information assumes a standard deviation of 1.0 / mm^8. Construct a 95% confidence interval for the expected value of the current white blood cell levels of this population.

2. Explain in your own words what does it mean? this confidence interval?

Answer 1

1)
sample mean, xbar = 4.738
sample standard deviation, σ = 1
sample size, n = 10

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 1/sqrt(10)
ME = 0.62

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (4.738 - 1.96 * 1/sqrt(10) , 4.738 + 1.96 * 1/sqrt(10))
CI = (4.12 , 5.36)

2)

we are 95% confident that the current white blood cell levels of this population. is between 4.12 and 5.36