for a confidence level of 98% with a sample size of 13, find the critical t value.
for a confidence level of 98% with a sample size of 13, find the critical t value.
Answer
Explanation:
Step1: Calculate degrees of freedom
The degrees of freedom $df=n - 1$, where $n = 13$. So $df=13 - 1=12$.
Step2: Determine the significance level
The confidence level is $C = 0.98$. The significance level $\alpha=1 - C=1 - 0.98 = 0.02$. Since it is a two - tailed test (common in confidence interval problems), we divide $\alpha$ by 2, so $\frac{\alpha}{2}=\frac{0.02}{2}=0.01$.
Step3: Look up the t - value
We use the t - distribution table or a statistical software/ calculator. Looking up the t - value with $df = 12$ and right - tail area $\frac{\alpha}{2}=0.01$, we find the critical t - value. Using a t - distribution table or a calculator like TI - 84 Plus (invT(1 - 0.01, 12)), the critical t - value is approximately $t_{\alpha/2}= 2.681$.
Answer:
$2.681$