Question

A retrospective study of 159 pairs of twins was performed. The twin pairs each had one male child and one female child. Their birth weights were studied to determine if the male twin was consistently heavier.

The difference in weights was calculated by subtracting the female weight (in ounces) from the male weight (in ounces):

d=xm-xf

After looking at 159 pairs of twins, the study finds the 99% confidence interval for the mean difference of weights (in ounces) is:

2.4 < μd < 6

Can we be reasonably sure that the male twins are heavier than the females?

• Yes
• No

Why or why not?

Answer 1

Solution:

Given: The twin pairs each had one male child and one female child. Their birth weights were studied to determine if the male twin was consistently heavier.

The difference in weights was calculated by subtracting the female weight (in ounces) from the male weight (in ounces):

d=x_m-x_f

The 99% confidence interval for the mean difference of weights (in ounces) is:

2.4 < μ_d < 6

We have to determine  if the male twin was consistently heavier.

If confidence interval include number 0, then we say there is no difference in both variables under study.

If confidence interval has both negative values, then first variables has values smaller than second variable.

If confidence interval has both positive values, then first variables has values larger  than second variable.

Since given confidence interval is: 2.4 < μ_d < 6 has both positive values, thus male twins have more weight than female weight , because we have taken difference of Male weight - Female Weight.

Thus we can be reasonably sure that the male twins are heavier than the females.

Thus answer is: Yes