Question

A naturalist wants to determine the mean gestation period of a type of fox. It is known that the distribution of gestation time is normal with standard deviation of 7 days. The researcher looks at a random sample of 20 foxes and finds the mean gestation time is 108 days. Find a 90% confidence interval for the mean gestation period of foxes.  

Answer 1

b )Given that,

= 108

s =7

n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,19 = 1.729    ( using student t table)

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

= 1.729 * ( 7/ 20) = 2.7

The 90% confidence interval mean is,

- E < < + E

108-2.7 < <108 + 2.7

(105.3,110.7)