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.

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.

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.

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.

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.