Question

Beavers are the only other animal besides humans that dramatically change the environment to build their communities. A biologist interested in the sleep patterns of beavers, randomly selected 12 adult beavers to study. Each beaver was fitted with a small device to measure sleep and returned to the wild. The mean number of hours per day spent sleeping was recorded as 8.2 with a standard deviation of 1.4 hours. Assuming all conditions have been met, what is the result in a 90% confidence interval for the mean number of hours of sleep for an adult beaver?
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Answer 1

Solution :

Given that,

= 8.2

s = 1.4

n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,11 = 1.796

Margin of error = E = t_/2,df * (s /n)

= 1.796 * (1.4 / 12)

= 0.726

The 90% confidence interval estimate of the population mean is,

- E < < + E

8.2 - 0.726 < < 8.2 + 0.726

7.474 < < 8.926

(7.474, 8.926)