To determine the proper order of the given critical values from least to greatest, let us compare the magnitudes of each value. The critical values are as follows:
1. [tex]\( t_{0.05} \)[/tex] with 10 degrees of freedom: approximately 1.8125
2. [tex]\( t_{0.05} \)[/tex] with 14 degrees of freedom: approximately 1.7613
3. [tex]\( Z_{0.05} \)[/tex]: approximately 1.6449
Comparing the numerical values:
- [tex]\( 1.6449 < 1.7613 < 1.8125 \)[/tex]
Thus, the correct order from least to greatest is:
[tex]\[ Z_{0.05} < t_{0.05} \text{ with 14 degrees of freedom} < t_{0.05} \text{ with 10 degrees of freedom} \][/tex]
Therefore, the correct answer is:
F. [tex]\( Z_{0.05} < t_{0.05} \text{ with 14 degrees of freedom} < t_{0.05} \text{ with 10 degrees of freedom} \)[/tex]
