Question

Comparing Birth Weights The birth weights of a sample of males have a mean of 3272.8 g and a standard deviation of 660.2 g. The birth weights of a sample of females have a mean of 3037.1 g and a standard deviation of 706.3 g (based on Data Set 4 “Births” in Appendix B). When considered among members of the same gender, which baby has the relatively larger birth weight: a male with a birth weight of 3400 g or a female with a birth weight of 3200 g? Why?

Short answer

The birth weight of the female is greater than that of the male.

Step-by-step solution

Given information

The mean birth weight for males is 3272.8 g.

The mean birth weight for females is 3037.1 g.

The standard deviation of the birth weight for males is 660.2 g.

The standard deviation of the birth weight for females is 706.3 g.

The birth weight of male is 3400 g and that of female is 3200 g.

Explanation for the z-score

The z-score is computed as shown below.

$z=\frac{x-\overline{x}}{s}...\left(1\right)$

For the difference between observed and mean values over the standard deviation value.

Define the values of measures

Define F and M as the random variables for the birth weights of females and males.

Also, ${\overline{x}}_F,{\overline{x}}_M$ are the sample mean values for the random variables F and M, respectively.

Similarly, $s_F,s_M$are the sample standard deviations for the random variables F and M, respectively.

Thus,

$$\begin{gathered} {\overline{x}}_M=3272.8 \\ {s}_M=660.2 \\ {\overline{x}}_F=3037.1 \\ {s}_F=706.3 \end{gathered}$$

The birth weight for female is 3200 g(f) and for male is 3400 g(m) .

Compute the z-score for each birth weight

The z-score for the birth weight of male is obtained using equation (1).

$$\begin{gathered} z_M=\frac{m-{\overline{x}}_M}{s_M} \\ =\frac{3400-3272.8}{660.2} \\ =0.193 \end{gathered}$$

The z-score for the birth weight of female is also obtained using equation (1).

$$\begin{gathered} z_F=\frac{f-{\overline{x}}_F}{s_F} \\ =\frac{3200-3037.1}{706.3} \\ =0.231 \end{gathered}$$

Thus, the z-score for the male is 0.19 and for the female is 0.23.

Compare the weights in two genders

The weights are compared using the z-scores of both genders.

The z-score for male is lesser than the z-score for female as 0.19 is lesser than 0.23.

Thus, on the basis of the z-score, the birth weight of female is relatively greater than that of male.