Question

9) A zoologist weights 15 newborn African elephants born in captivity. The mean weight of the sample is 184 lbs with a standard deviation of 6.7 lbs.

a) Find a 99% confidence interval for the true weight of newborn African elephants born in captivity.

b) Provide the margin of error of the interval as your answer.

Round your answer to 1 decimal place.

Answer 1

Given that,

= 184

s =6.7

n = 15

Degrees of freedom = df = n - 1 = 15- 1 = 14

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_{t /2  df} = t_0.005, 14= 2.977 ( using student t table)

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

= 2.977 * (6.7 / 15)

E= 5.2

The 99% confidence interval estimate of the population mean is,

- E < < + E

184 - 5.2 < < 184+ 5.2

178.8 < < 189.2

( 178.8 ,189.2 )