Question

Large samples of women and men are obtained and the hemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means (µ1 − µ2), where the measures from women correspond to population 1 and the measures from men correspond to population 2: (−1.76 g/dL, −1.62 g/dL) 1. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men? 2. Express the confidence interval with measures from men being population 1 and measures from women being population 2.

Answer 1

Men in general have more hemoglobin than women.

Explanation:

Given that large samples of women and men are obtained and the hemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means (µ1 − µ2), where the measures from women correspond to population 1 and the measures from men correspond to population 2:

Confidence interval =
`(−1.76 g/dL, −1.62 g/dL)`

This suggest on an average women have less haemoglobin than men.

Since lower bound is -1.76 and upper bound is -1.62, and 0 does not belong to this interval, this implies that we are 95% confidence that for large samples of men and women women tend to have less haemoglobin than men.

2) If we change men and women confidence interval would become

`( 1.62 g/dL,1.76 g/dL)`

with positive signs and bounds adjusted accordingly(reversed)