Question

The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds.

A) Construct a 95% confidence interval for the population mean weight of newborn elephants.

B) What will happen to the confidence interval obtained, if 500 newborn elephants are weighed instead of 50? Why?

Answer 1

a)

sample mean, xbar = 244
sample standard deviation, s = 11
sample size, n = 50
degrees of freedom, df = n - 1 = 49

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.01

ME = tc * s/sqrt(n)
ME = 2.01 * 11/sqrt(50)
ME = 3.127

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (244 - 2.01 * 11/sqrt(50) , 244 + 2.01 * 11/sqrt(50))
CI = (240.87 , 247.13)

b)

If we increase the sample size the interval becomes narrower