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 $-1.76\text{g/dL}<{\mu }_1-{\mu }_2<-1.62\text{g/dL}$, where the measures from

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

a. As the value 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 with 95% 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:

$-1.76g/dL<{\mu }_1-{\mu }_2<-1.62g/dL$

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.