## The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval fo

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.)

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1 week 2021-09-15T14:45:52+00:00 1 Answer 0

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 level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

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

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.