Question

Confidence Interval for Haemoglobin

Large samples of women and men are obtained, and the haemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:\(\)\( - 1.76g/dL < {\mu _1} - {\mu _2} < - 1.62g/dL\).

a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?

b. Write a brief statement that interprets that confidence interval.

c. Express the confidence interval with measures from men being population 1 and measures from women being population 2.

Short answer

a. The confidence interval shows that there is a significant difference between the mean hemoglobin level in women and men.

b. The interval would contain the actual difference of mean hemoglobin measures for women and men.

c. The hemoglobin level of men being population 1 is greater than the hemoglobin level of women being population 2.

Step-by-step solution

Given information

The confidence level is 95%.

The confidence interval is \( - 1.76\;{\rm{g/dL}} < {\mu _1} - {\mu _2} < - 1.62\;{\rm{g/dL}}\), where the measures from

women correspond to population 1, and the measures from men correspond to population 2.

Test the claim from confidence interval

a. As thevalue 0 does not belong to the interval, it can be concluded that there is a significant difference between the mean hemoglobin level in women and men.

Interpret confidence interval

b. The 95% confidence interval for the difference of mean implies that it can be stated with95% confidence that the actual difference of the mean haemoglobin levelsfor women and men would lie between -1.76 and -1.62.

Express confidence interval in terms of populations

c.Here, the confidence interval is expressed as:

\( - 1.76{\rm{g/dL < }}{\mu _1} - {\mu _2} < - 1.62{\rm{g/dL}}\)

Where, -1.76 and -1.62 are the lower and upper measures.

The measures are negative, which implies that the mean hemoglobin level of population 2 is greater than the hemoglobin level of population 1.

So, the mean level of hemoglobin is higher for men than women.