Question

# The standard deviation of the weights of elephants is known to be approximately 15 pounds. We...

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?

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

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