Question

find the critical value, ( t_{c} ) for ( c = 0.99 ) and ( n = 10 ).
a. 2.262
b. 1.833
c. 3.169
d. 3.250

Explanation:

Step1: Calculate the degrees of freedom

Degrees of freedom \(df=n - 1\). Given \(n = 10\), so \(df=10-1 = 9\).

Step2: Determine the significance level

The confidence level \(c = 0.99\), so the significance level \(\alpha=1 - c=1 - 0.99=0.01\). Since it is a two - tailed test (common in critical value problems when not specified otherwise), \(\frac{\alpha}{2}=\frac{0.01}{2}=0.005\).

Step3: Look up the \(t\) - value in the \(t\) - distribution table

Using the \(t\) - distribution table with \(df = 9\) and \(\frac{\alpha}{2}=0.005\), we find the critical value \(t_c\).

Answer:

D. 3.250