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. State the confidence interval. (Round your answers to two decimal places.)

Answer 1

Answer:

The 95% confidence interval for the population mean weight of newborn elephants is between 242.12 pounds and 245.88 pounds.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.025 = 0.975$, so $z = 1.96$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{15}{244} = 1.88$

The lower end of the interval is the sample mean subtracted by M. So it is 244 - 1.88 = 242.12 pounds.

The upper end of the interval is the sample mean added to M. So it is 244 + 1.88 = 245.88 pounds

The 95% confidence interval for the population mean weight of newborn elephants is between 242.12 pounds and 245.88 pounds.