91Ó°ÊÓ

A contains degrees of freedom from $1$ to $75$ in order, but only chosen degrees of freedom after that.

$t-$value and $z-$ value concept used.

Because we can utilize the linear interpolation method or technology to find the $t-$values for those degrees of freedom that are not shown in the table. Additionally, for degrees of freedom greater than $2000$, the $t$and $z$values are nearly equivalent. As a result, the $t$table does not include $t$ values for all degrees of freedom.

Because consecutive entries, i.e. consecutive $t-$values, are significantly different for fewer degrees of freedoms, but (roughly) the same for bigger degrees of freedoms.

We would use the value of $t_{0.05}$corresponding to $df=85$i.e., $1.292$

Because, $85$is the nearest to the $df87$

$∴$For $df=87,t_{0.05}=1.292$

Similarly, for $t_{0.05}$with $df=125$we would use the value of $t_{0.05}$with $df=100$i.e., $1.660$$∴$For $df=125,t_{0.05}=1.660$

For $t_{0.05}$with $df=650$, we would use the value of $t_{0.05}$for $df=600$or $700$, because both are same.

$∴$For $df=650,t_{0.05}=1.647$

We'd use $z_{0.05}$, or $1.645$, for $t_{0.05}$with $df=3000$because for degrees of freedom more than $2000$, we'd use $z_{0.05}$, or $1.645$

There is no difference between $t-$value and $z-$value.

$⇒\text{For}df=3000,t_{0.05}=1.645$