Question

In Exercises 13–16, use z scores to compare the given values.

Red Blood Cell Counts Based on Data Set 1 “Body Data” in Appendix B, males have red blood cell counts with a mean of 4.719 and a standard deviation of 0.490, while females have red blood cell counts with a mean of 4.349 and a standard deviation of 0.402. Who has the higher count relative to the sample from which it came: a male with a count of 5.58 or a female with a count of 5.23? Explain.

Short answer

The female red blood cell count of 5.23 is higher.

Step-by-step solution

Given information

The red blood cell counts of a set of males and females are provided.

The mean male red blood cell count is given to be equal to 4.719, and the corresponding standard deviation is 0.490.

The mean female red blood cell count is given to be equal to 4.349, and the corresponding standard deviation is 0.402.

Compute the z-scores for the male and female red blood cell counts

Thez-score is the value that provides an idea of where a given value lies relative to the mean value. Statistically,

$z=\frac{x-\overline{x}}{s}$

For larger values of z-score (in absolute terms), the related data values are farther away from the mean and hence, more extreme.

The z-score for male red blood cell count is:

$$\begin{gathered} z=\frac{x-\overline{x}}{s} \\ =\frac{5.58-4.719}{0.490} \\ =1.76 \end{gathered}$$

Therefore, thez-score for male red blood cell count equal to 5.58 is 1.76.

The z-score for female red blood cell count is:

$$\begin{gathered} z=\frac{x-\overline{x}}{s} \\ =\frac{5.23-4.349}{0.402} \\ =2.19 \end{gathered}$$

Therefore, the z-score for female red blood cell count equal to 5.23 is 2.19.

Comparison

The female red blood cell count equal to 5.23 is 2.19 standard deviations above the mean, and the male red blood cell count equal to 5.58 is 1.76 standard deviations above the mean.

As 5.23 is farther from the mean value as compared to 5.58, thefemale red blood cell countof 5.23 is higher.