Question

question 1
for the following parameters, find the critical value t from students t - distribution table:
n = 8 and confidence level = 95%
critical value t = ______

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \( df=n - 1\). Given \(n = 8\), so \(df=8 - 1=7\).

Step2: Determine significance level

Confidence level \(C = 95\%=0.95\). Significance level \(\alpha=1 - C=1 - 0.95 = 0.05\). For a two - tailed test (common in confidence interval for mean when population standard deviation is unknown), the area in each tail is \(\frac{\alpha}{2}=\frac{0.05}{2}=0.025\).

Step3: Look up in t - distribution table

Using a t - distribution table (or statistical software), with \(df = 7\) and \(\frac{\alpha}{2}=0.025\), we find the critical value.

Answer:

\(2.365\)