Questions: A group of adult males has foot lengths with a mean of 26.69 cm and a standard deviation of 1.16 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 23.9 cm significantly low or significantly high? Explain. Significantly low values are cm or lower. (Type an integer or a decimal. Do not round.) Significantly high values are cm or higher. (Type an integer or a decimal. Do not round.) Select the correct choice below and fill in the answer box(es) to complete your choice. A. The adult male foot length of 23.9 cm is significantly high because it is greater than cm. (Type an integer or a decimal. Do not round.) B. The adult male foot length of 23.9 cm is not significant because it is between cm and cm. (Type integers or decimals. Do not round.) C. The adult male foot length of 23.9 cm is significantly low because it is less than cm. (Type an integer or a decimal. Do not round.)

A group of adult males has foot lengths with a mean of 26.69 cm and a standard deviation of 1.16 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 23.9 cm significantly low or significantly high? Explain.

Significantly low values are  cm or lower.
(Type an integer or a decimal. Do not round.)
Significantly high values are  cm or higher.
(Type an integer or a decimal. Do not round.)
Select the correct choice below and fill in the answer box(es) to complete your choice.
A. The adult male foot length of 23.9 cm is significantly high because it is greater than  cm.
(Type an integer or a decimal. Do not round.)
B. The adult male foot length of 23.9 cm is not significant because it is between  cm and  cm.
(Type integers or decimals. Do not round.)
C. The adult male foot length of 23.9 cm is significantly low because it is less than  cm.
(Type an integer or a decimal. Do not round.)
Transcript text: A group of adult males has foot lengths with a mean of 26.69 cm and a standard deviation of 1.16 cm . Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 23.9 cm significantly low or significantly high? Explain. Significantly low values are $\square$ cm or lower. (Type an integer or a decimal. Do not round.) Significantly high values are $\square$ cm or higher. (Type an integer or a decimal. Do not round.) Select the correct choice below and fill in the answer box(es) to complete your choice. A. The adult male foot length of 23.9 cm is significantly high because it is greater than $\square \mathrm{cm}$. $\square$ (Type an integer or a decimal. Do not round.) B. The adult male foot length of 23.9 cm is not significant because it is between $\square$ cm and $\square$ cm . (Type integers or decimals. Do not round.) C. The adult male foot length of 23.9 cm is significantly low because it is less than $\square \mathrm{cm}$. $\square$ (Type an integer or a decimal. Do not round.)
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Solution

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Solution Steps

Step 1: Calculate Significantly Low and High Values

Using the range rule of thumb, we can identify the limits for significantly low and significantly high values based on the mean (\( \mu \)) and standard deviation (\( \sigma \)) of the foot lengths. The calculations are as follows:

  • Significantly low values are defined as: \[ \text{Significantly Low} = \mu - 2\sigma = 26.69 - 2 \times 1.16 = 24.37 \text{ cm} \]

  • Significantly high values are defined as: \[ \text{Significantly High} = \mu + 2\sigma = 26.69 + 2 \times 1.16 = 29.01 \text{ cm} \]

Step 2: Evaluate the Given Foot Length

We need to determine if the adult male foot length of \( 23.9 \) cm is significantly low, significantly high, or not significant.

  • Comparing \( 23.9 \) cm with the calculated limits:
    • Since \( 23.9 \) cm is less than \( 24.37 \) cm, we conclude that: \[ 23.9 \text{ cm} < 24.37 \text{ cm} \] Thus, \( 23.9 \) cm is significantly low.

Final Answer

The limits separating values that are significantly low or significantly high are:

  • Significantly low values are \( 24.37 \) cm or lower.
  • Significantly high values are \( 29.01 \) cm or higher.

The adult male foot length of \( 23.9 \) cm is significantly low because it is less than \( 24.37 \) cm.

\(\boxed{\text{Significantly low values: } 24.37 \text{ cm}; \text{ Significantly high values: } 29.01 \text{ cm}; \text{ Conclusion: significantly low.}}\)

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