A group of adult males has foot lengths with a mean of 26.68 cm and a standard deviation of 1.49cm. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 23.4 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 23.4 cm is significantly low because it is less than ? cm.
(Type an integer or a decimal. Do not round.)
B.The adult male foot length of
23.4 cm is significantly high because it is greater than ? cm.
(Type an integer or a decimal. Do not round.)
C.The adult male foot length of
23.4 cm is not significant because it is between ? cm and ? cm.
(Type integers or decimals. Do not round.)
The range of rule of thumb says that the appropriate range for majority of the values is within 2 standard deviations of the mean.
Therefore significantly lower values are the ones which are more
than 2 standard deviations less than the mean. This cutoff
therefore is computed here as:
= 26.68 - 2*1.49 = 23.7
therefore Values < 23.7cm are significantly low values.
Similarly for significantly high values,
= 26.68 + 2*1.49 = 29.66
Therefore values > 29.66 cm are significantly high values.
The z score for 23.4cm is computed here as:
z = (23.4 - 26.68) / 1.49 = -2.2 < -2
As the z score here is more than 2 standard deviations less than the mean, therefore it is a significantly low. Also as it is less than 23.7cm.
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