Answer:
Given Information from Question:
The Sample Mean $(x\bar)=13.4$
The Sample Standard Deviation $(s)=3.5$
The Sample Size $(n)=77$
The Confidence Interval level $=99%$
The critical value at significance level = 1-0.99 = 0.01, and df = n – 1 = 77-1 = 76, The critical value is:
$t_c = t_{\frac{\alpha}{2}, \text{df}} = t_{0.01/2, 76} = 2.642$
The confidence interval:
$CI = \overline{x} \pm t_c \times \frac{s}{\sqrt{n}} = 13.4 \pm 2.642 \times \frac{3.5}{\sqrt{77}} = (12.3462, 14.4538) $
