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.

Answer 1

Answer:

95% confidence interval for the mean weight of newborn elephant calves is between a lower limit of 240.87 pounds and an upper limit of 247.13 pounds.

Step-by-step explanation:

Confidence Interval = mean + or - Error margin (E)

mean = 244 pounds

sd = 11 pounds

n = 50

degree of freedom = n - 1 = 50 - 1 = 49

Confidence level = 95%

t-value corresponding to 49 degrees of freedom and 95% confidence level is 2.010

E = t×sd/√n = 2.010×11/√50 = 3.13 pounds

Lower limit = mean - E = 244 - 3.13 = 240.87 pounds

Upper limit = mean + E = 244 + 3.13 = 247.13 pounds

95% confidence interval is between 240.87 and 247.13 pounds.