Question

Males have red blood cell counts with a mean of 4.719 and a standard deviation of .490, while females have red blood cell counts with a mean of 4.349 and a standard deviation of .402. Who has the higher count relative to the sample from which it came, the male with a count of 5.58 or a female with a count of 5.23

Answer 1

Answer:

• The female  has a higher count relative to the sample of females than the male relative to the sample of males.

Explanation:

When you want to compare the means of two samples with different statistics you may use the z-score.

The z-score measures how far a value (data point) is from the mean, in terms of the standard deviation.

The z-score is calculated as:

          $z-score=(x-\mu )}/\sigma$

Where:

          $x=\text{value of the data}\\\\\mu =mean\\\\\sigma = \text{standard deviation}$

1. Male with a count of 5.58

       $z-score=(5.58-4.719)/0.490=1.757$

2. Female with a count of 5.23

     $z-score=(5.23-4.349)/0.402=2.192$

Therefor, the z-score of the female is greater than the z-score of the male.

The greater z-score means that, relative to her group, the female has a higher count than the male.