Question

Zoologists studied the characteristics of the burrow systems of a subterranean rodent. A sample of 51 burrows had their​ depths, in​ centimeters, recorded in the following table. 15.8, 15.9, 18.9, 18.4, 13.6, 15.6, 14.6, 12.2, 11.1, 12.9, 17.1, 16.3, 16.5, 16.3, 12.0, 14.4, 15.4, 13.1, 17.3, 12.2, 18.9, 16.1, 13.2, 14.9, 14.3, 12.6, 11.2, 16.7, 17.6, 8.1, 19.3, 17.5, 15.3, 15.6, 19.7, 14.3, 12.9, 12.8, 13.7, 16.3, 17.7, 13.8, 14.1, 16.6, 11.7, 15.9, 16.8, 9.2, 15.4, 18.2, 14.4.

Find and interpret a 99​% confidence interval for the mean depth of all subterranean rodent burrows. The 99​% confidence interval for μ is from __ to __. (Round to 3 decimal points as needed)

Answer 1

Answer)

First we need to find the mean and standard deviation of the given data

Mean = 14.988

S.d = 2.545

As the population standard deviation is unknown we will use t distribution table to construct the interval

Degrees of freedom is = n-1, 50

For DF 50 and 99% confidence level, critical value t is = 2.678

Margin of error (MOE) = t*(s.d/√n)

= 2.678*(2.545/√51)

= 0.95436229154

Confidence interval is given by

(Mean - moe) to (mean + MOE)

14.0336377084 to 15.9423622915

14.034 to 15.942