Question

The​ world's smallest mammal is the bumblebee​ bat, also known as the​ Kitti's hog-nosed bat​ (or Craseonycteris thonglongyai as it is affectionately​ called). Such bats are roughly the size of a large bumblebee. Listed below are weights​ (in grams) from a sample of these bats. Construct 95% confidence interval estimate of the standard deviation of weights for all such bats. Assume that the sample is a simple random sample obtained from a population with a normal distribution.

1.7 1.7 1.5 2.0 2.3 1.6 1.6 1.9 1.4 1.6 2.2 1.4 1.7 1.6 1.6

The 95% confidence interval estimate is _ g < sigma < _ g

Answer 1

Solution:

The 95% confidence interval estimate is:

$\large \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\frac{0.05}{2}}}}< \sigma<\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\frac{0.05}{2}}}}$

(15-100.26782 26,119 (15-100.26782 15.629

0.196 «σ<0.422

Therefore, the 95% confidence interval estimate is 0.196 g < sigma < 0.422 g