To determine the total number of penguins measured for the sample, we need to understand the information provided in an ANOVA table. Specifically, the degrees of freedom (df) in the ANOVA table help us to deduce the total number of observations.
In an ANOVA table:
- Total degrees of freedom (df_total) is calculated as the total number of observations minus 1.
- Between-group degrees of freedom (df_between) is usually the number of groups minus 1.
- Within-group degrees of freedom (df_within) is the total number of observations minus the number of groups.
The sum of the between-group degrees of freedom and within-group degrees of freedom gives us the total degrees of freedom:
[tex]\[ \text{df_total} = \text{df_between} + \text{df_within} \][/tex]
To find the total number of observations (n), we use:
[tex]\[ \text{df_total} = n - 1 \][/tex]
Given the data, we have a specific value for the total degrees of freedom, which we'll call df_total.
Given that df_total is 338:
[tex]\[ 337 + 2 = 339 \][/tex]
Thus, the total number of penguins measured for the sample is:
[tex]\[ \boldsymbol{n = 339} \][/tex]
So, the correct answer is:
b. 339
