Question

The length (in cm) of 12 fishes caught from a lake is given as follows:

9.8, 9.1, 9.1, 11.3, 10.7, 10.2, 10.1, 9.7, 9.9, 9.5, 10.4, 10.5

Assume the population follows a normal distribution with variance of 4 cm. Calculate the 99% confidence interval to estimate the true mean length for all fishes in that lake.

Answer 1

calculating the confidence interval about the population mean at 99% level.

$\text {confidence interval}=\bar x ± z_{\frac {\alpha}{2}} \frac{\sigma}{\sqrt {n}}$

$\bar x= \frac{\sum x}{n}=\frac{9.8+9.1+9.1+...+10.5}{12}$ =10.025

The critical value at 99% level=2.576

$CI=10.025± 2.576 \frac{2}{\sqrt{12}}$

= 10.025± 1.487

=(8.537, 11.512)