Q.3.3 - The Practice of Statistics for AP

Question

Construct a $95\%$ confidence interval for$M.$ Show your method 

Step-by-Step Solution

Answer

The obtained confidence interval is $(22.338,29.962)$

Step 1: Given information

Given in the question that, Biologists studying the healing of skin wounds measured the rate at which new cells closed a cut made in the skin of an anesthetized newt. Here are data from a random sample of $18$ newts, measured in micrometers (millionths of a meter) per hour:

$20 29 27 34 40 22 28 14 35 26 35 12 30 23 18 11 22 23 33$

Step 2: Explanation

The given dataset is

$29$

$27$

$34$

$40$

$22$

$28$

$14$

$35$

$36$

$35$

$12$

$30$

$23$

$18$

$11$

$22$

$23$

$33$

The formula to compute the confidence interval is:

$\overline{x}-t_{\frac{a}{2}}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\frac{a}{2}}\times \frac{s}{\sqrt{n}}$

The output obtained using $\mathrm{Ti}-83$ calculator is:

Thus, the obtained confidence interval is $(22.338,29.962)$.