Question

Assessment of Objective 3: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are 15 18 16 19 14 12 14 17 15 11 Using a=0.01, does this information indicate the population average HC for this patient is higher than 14?

Answer 1

x̅ (Using Excel function AVERAGE( )) = 15.1

s (Using Excel function STDEV.S( )) = 2.514

n = 10, μ = 14, Degrees of freedom: df = n-1 = 9

Level of significance = 0.01

H₀: μ < 14, Population average HC is not higher than 14

H₁: μ > 14, Population average HC is higher than 14

Test statistic: t = (x̅-μ)/(s/n^0.5) = (15.1-14)/(2.514/10^0.5) = 1.384

Critical value (Using Excel function ABS(T.INV(probability,df))) = ABS(T.INV(0.01,9)) = 2.821

Since test statistic is less than critical value, we do not reject the null hypothesis.

So, μ < 14, population average HC is not higher than 14.