Question

for parts a and b, use technology to estimate the following
a) the critical value of t for a 99% confidence interval with df = 6
b) the critical value of t for a 95% confidence interval with df = 106
a) what is the critical value of t for a 99% confidence interval with df = 6?
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for confidence interval

The formula for a confidence interval using the t - distribution is \(\bar{x}\pm t_{\alpha/2}\frac{s}{\sqrt{n}}\), where \(t_{\alpha/2}\) is the critical value. For a \(C = 99\%\) confidence interval, \(\alpha=1 - C=1 - 0.99 = 0.01\), and \(\alpha/2=0.005\). The degrees of freedom \(df = 6\).

Step2: Use technology (e.g., t - distribution tables or statistical software)

Using a t - distribution table or software (such as Excel: =T.INV.2T(0.01,6) or R: qt(0.005,6,lower.tail = FALSE)).
When we calculate, we find that \(t_{0.005,6}=3.71\)

Answer:

\(3.71\)