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. Round all answers to the nearest hundredth. Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between?

Answer 1

Confidence interval is written as

point estimate ± margin of error

In this case, the point estimate is the sample mean

the formula for calculating margin of error is expressed as

`\text{margin of error = z }*\frac{\sigma}{\sqrt[]{n}}`

where

σ = population standard deviation

n = sample size

z is the z score corresponding to a 95% confidence level. From the standard normal distribution table, z = 1.96

From the information given,

σ = 15

n = 50

sample mean = 244

By substituting these values into the formula,

`\text{margin of error = 1.96 }*\frac{15}{\sqrt[]{50}}\text{ = 4.16}`

Thus,

confidence interval = 244 ± 4.16

Lower limit of conidence interval = 244 - 4.16 = 239.84

Upper limit of conidence interval = 244 + 4.16 = 248.16

Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between 239.84 pounds and 248.16 pounds