Question

Let x be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has an approximately normal distribution with a population mean of μ=14.2μ=14.2, and population standard deviation of σ=2.4σ=2.4. Suppose a female patient had 10 blood tests over the past year, and the sample mean HC was determined to be x¯¯¯=15.2x¯=15.2.

1. What is the value of the sample test statistic (z)?
2. What is the P-value of the test?
3. At a significance level of 0.05, what can we conclude about the HC of the female patient?
   We conclude that her HC is  ? higher not higher lower  than the population average.

• Your answers must be accurate to the nearest hundredth.

Answer 1

a) The test statistic here is computed as:

Therefore 1.32 is the test statistic value here.

b) The p-value here is computed from the standard normal tables as:
p = P(Z > 1.32) = 0.0938

Therefore 0.0938 is the required p-value here.

c) As the p-value here is 0.0938 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here.

Therefore we cannot conclude here anything as the test is not significant here and we dont have insufficient evidence here.