Question

In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high

Foot Lengths Based on Data Set 2 “Foot and Height” in Appendix B, adult males have foot lengths with a mean of 27.32 cm and a standard deviation of 1.29 cm. Is the adult male foot length of 30 cm significantly low or significantly high? Explain.

Short answer

The lower limit is equal to 24.74 cm, and the upper limit is equal to 29.90 cm.

The value equal to 30 cm is significantly high.

Step-by-step solution

Given information

A sample of male foot lengths is provided.

The mean male foot length is equal to 27.32 cm.

The standard deviation of the male foot length is equal to 1.29 cm.

Identifying the limits 

The range rule of thumb is used to identify significant values.

The limits that separate the significant values are given as follows:

• The upper limit is equal to$\mu +2\sigma$ .
• The lower limit is equal to$\mu -2\sigma$ .

If a value is equal to or above the upper limit, it is considered significantly high.

If a value is equal to or below the lower limit, it is considered significantly low.

If a value is between the limits, it is considered insignificant.

For the given sample, the limits are calculated as follows:

Lower limit:

$$\begin{gathered} \mu -2\sigma =27.32-2\times 1.29 \\ =27.32-2.58 \\ =24.74 \end{gathered}$$

Upper limit:

$$\begin{gathered} \mu +2\sigma =27.32+2\times 1.29 \\ =27.32+2.58 \\ =29.90 \end{gathered}$$

Therefore, the limits separating significant values are (24.74cm,29.90 cm).

Checking for significance

As the value of 30 cm lies above the upper limit of 29.90 cm, it issignificantly high.