Question

Let x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population.

[18, 15 , 21, 14, 15, 19, 18, 18, 12, 11]

State the null and alternate hypothesis, give the p-value and state your conclusion based on a 5% significance level.

a) H_o: μ = 14, H_a: μ < 14; p-value = 0.034; reject H_o at the 5% significance level

b) H_o: μ = 14, H_a: μ > 14; p-value = 0.034; reject H_o at the 5% significance level

c) H_o: μ = 16.1, H_a: μ ≠ 16.1; p-value = 0.069; fail to reject H_o at the 5% significance level

d) H_o: μ = 14, H_a: μ ≠ 14; p-value = 0.069; fail to reject H_o at the 5% significance level

e) H_o: μ = 16.1, H_a: μ > 16.1; p-value = 0.034; reject H_o at the 5% significance level

Answer 1

Research question - If the female patient has significantly high HC compared to the population.

The appropriate Hypotheses are,

H_o: μ = 14, H_a: μ > 14;

From the data,

Sample mean, = 16.1

T

Sample Standard deviation, s = 3.213

Standard error of mean, SE = s / $\sqrt{n}$ = 3.213 / = 1.01604

V10

Test statistic, t = (
T
- $\mu$ ) / SE = (16.1 - 14) / 1.01604 = 2.07

Degree of freedom = n-1 = 10-1 = 9

p-value = P(t > 2.07, df = 9) = 0.034

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 at the the 5% significance level, and conclude that there is significant evidence that the female patient has significantly high HC compared to the population.

The answer is,

b) H_o: μ = 14, H_a: μ > 14; p-value = 0.034; reject H_o at the 5% significance level