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. construct a 95% confidence interval for the population mean weight of newborn elephants. state the confidence interval. (round your answers to two decimal places.) ,

The confidence interval is [240.87 , 247.13].

Step-by-step explanation:

Given : 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.

To find : Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval?

Solution :

We have given that,

Sample mean, x =244

Standard deviation, s =11

Sample size, n =50

First we find the standard error,

Then we find the margin of error,

Applying t-table values,

is the t-table value

Level of significance,

From standard normal table, two tailed value of with n-1 = 49 d.f is

Substitute in the formula,

Now, The confidence of the interval is given by,

Therefore, The confidence interval is[ 240.87 , 247.13 ].