Answer
$ \begin{array}{ll}
a. & 1.761\\
b. & 2.807 \\
c. & \pm 2.771\\
d. & \pm 2.583
\end{array}$
Work Step by Step
For each part, use the table for the $t$-distribution.
Recall that t-values in the left tail are negative, and in the right tail, positive.
Also, recall that the test statistic follows a $t$-distribution with $n-1$ degrees of freedom.
$a.$
In the row
$d.f.= 15-1=14$,
find the intersection with the column "one tail, $\alpha=0.05$"
Critical value: $1.761$
$b.$
In the row
$d.f.=23-1=22$,
find the intersection with the column "one tail, $\alpha=0.005$"
Critical value: $2.807$
$c.$
In the row
$d.f.= 28-1=27$,
find the intersection with the column "two tails, $\alpha=0.01$"
Critical values: $\pm 2.771$
$d.$
In the row
$d.f.= 17-1=16$,
find the intersection with the column "two tails, $\alpha=0.002$"
Critical values: $\pm 2.583$
