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Put the following critical values in order from least to greatest:

- [tex]$t_{0.05}$[/tex] with 10 degrees of freedom
- [tex]$t_{0.05}$[/tex] with 14 degrees of freedom
- [tex]$Z_{0.05}$[/tex]

A. [tex]$t_{0.05}$[/tex] with 10 degrees of freedom [tex]$\ \textless \ t_{0.05}$[/tex] with 14 degrees of freedom [tex]$\ \textless \ z_{0.05}$[/tex]
B. [tex]$t_{0.05}$[/tex] with 14 degrees of freedom [tex]$\ \textless \ t_{0.05}$[/tex] with 10 degrees of freedom [tex]$\ \textless \ z_{0.05}$[/tex]
C. [tex]$z_{0.05} \ \textless \ t_{0.05}$[/tex] with 10 degrees of freedom [tex]$\ \textless \ t_{0.05}$[/tex] with 14 degrees of freedom
D. [tex]$t_{0.05}$[/tex] with 14 degrees of freedom [tex]$\ \textless \ z_{0.05} \ \textless \ t_{0.05}$[/tex] with 10 degrees of freedom
E. [tex]$t_{0.05}$[/tex] with 10 degrees of freedom [tex]$\ \textless \ z_{0.05} \ \textless \ t_{0.05}$[/tex] with 14 degrees of freedom
F. [tex]$z_{0.05} \ \textless \ t_{0.05}$[/tex] with 14 degrees of freedom [tex]$\ \textless \ t_{0.05}$[/tex] with 10 degrees of freedom

Sagot :

GinnyAnsweridn
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]
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