Question

find the critical value, $t_{c}$, for $c = 0.90$ and $n = 15$.

a. 2.624
b. 2.145
c. 1.761
d. 1.753

Explanation:

Step1: Calculate the degree of freedom

The degree of freedom \(df=n - 1\). Given \(n = 15\), then \(df=15-1 = 14\).

Step2: Determine the significance level

The confidence level \(c = 0.90\), so the significance level \(\alpha=1 - c=1 - 0.90=0.10\). And for a two - tailed t - distribution, \(\frac{\alpha}{2}=\frac{0.10}{2}=0.05\).

Step3: Look up the t - value in the t - distribution table

Using the t - distribution table with \(df = 14\) and \(\frac{\alpha}{2}=0.05\), we find the critical value \(t_{c}\).

Answer:

C. \(1.761\)