Question

find the critical t - value that corresponds to 95% confidence and n = 16. round to three decimal places

a. 2.947
b. 1.753
c. 2.131
d. 2.602

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \( df=n - 1\). Given \(n = 16\), so \(df=16 - 1=15\).

Step2: Determine significance level

For a 95% confidence level, the significance level \(\alpha=1 - 0.95 = 0.05\). Since it is a two - tailed test (common in confidence interval for means when population standard deviation is unknown), \(\alpha/2=0.025\).

Step3: Look up t - value

Using a t - distribution table or a calculator with t - distribution function (e.g., in R: qt(1 - 0.025, 15)), we find the critical t - value. For \(df = 15\) and \(\alpha/2=0.025\), the critical t - value is \(t_{0.025,15}=2.131\).

Answer:

C. 2.131