Question

find the critical value $t_{c}$ for the confidence level $c = 0.90$ and sample size $n = 15$. click the icon to view the t - distribution table. $t_{c}=\square$ (round to the nearest thousandth as needed.)

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom：$df=n - 1$. Given $n = 15$, so $df=15 - 1=14$.

Step2: Determine the significance level

Significance level：$\alpha=1 - c$. Given $c = 0.90$, so $\alpha=1 - 0.90 = 0.10$. And $\frac{\alpha}{2}=\frac{0.10}{2}=0.05$.

Step3: Find the critical value in the t - distribution table

Look up the value in the t - distribution table with $df = 14$ and the column corresponding to $\frac{\alpha}{2}=0.05$.

Answer:

$1.761$