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

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt n}$

$\overline{x}=\sum x_i/n=10$

critical values for 99% confidence interval:

$z=\pm 2.576$

$-2.576<\frac{10-\mu}{2/\sqrt{12}}<2.576$

$-1.49<10-\mu<1.49$

$8.51<\mu<11.49$