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A t-test is a statistical test for verifying hypothesis testing. It comes from t-distribution which varies according to its degrees of freedom.It is also used to compare the means of two groups.

By referring to the t-distribution table, we have to compute the probability,

$P\left(t猢�t_0\right)=.25withdf=15$

The value of that satisfies this equation is: -0.6912.

By referring to the t-distribution table, we have to compute the probability,

$P\left(t猢�t_0\right)=.1withdf=8$

The value of that satisfies this equation is: 1.39682.

By referring to the t-distribution table, we have to compute the probability,

$P\left(-t_0猢�t猢�t_0\right)=.01withdf=19$

The value of${\text{t}}_{\text{0}}$ that satisfies this equation is: 0.0127.

By referring to the t-distribution table, we have to compute the probability,

$P\left(-t_0猢�t猢�t_0\right)=.05withdf=24$

The value of that satisfies this equation is: 0.06337.