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, where the measures from women correspond to population 1 and the measures from men correspond to population​ 2:

negative 1.76 g divided by dL less than mu 1 minus mu 2 less than minus 1.62 g divided by dL

−1.76 g/dL<μ1−μ2<−1.62 g/dL. Complete parts​ (a) through​ (c) below.

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

Answer 1

Answer:

a) Because the confidence interval  does not include  0​ it appears that there

is  a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

b)There is​ 95% confidence that the interval from  −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2

c)   1.62 < μ1−μ2< 1.76

Step-by-step explanation:

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

Given:

95% confidence interval for the difference between the two population​ means:

−1.76g/dL< μ1−μ2 < −1.62g/dL

population 1 =  measures from women

population 2 =  measures from men

Solution:

a)

The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in​ men is not equal and that the  women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in​ men.

b)  

There is​ 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.

c)

If we interchange men and women then

• confidence interval range sign will become positive.
• μ1 becomes the population mean of the hemoglobin level in men
• μ2 becomes the population mean of the hemoglobin level in women
• So confidence interval becomes:

                                          1.62 g/dL<μ1−μ2<1.76 g/dL.

Answer 2

There is a significant difference between the mean level of hemoglobin in women and in men.

How to interpret the confidence interval

The confidence interval of the mean is given as:

$-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL$

The above confidence interval shows that the confidence interval is exclusive of 0.

This means that 0 is not part of the confidence interval

Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.

Read more about confidence intervals at:

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