Question

3. A random sample of wolf dens in the southwestern United States is taken. The number of pups found are:

5 8 7 5 3 4 3 9 5 8 5 6 5 6 4 7

a. Find a 90% confidence interval for the population mean number of wolf pups per den. Include the sample statistics, degrees of freedom, LaTeX: t_{\frac{\alpha}{2}}t α 2 , standard error and a sentence.
b. What sample size is needed for the margin of error to be 0.3?   

Answer 1

Here in this scenario A random sample of wolf dens in the southwestern United States is taken. Based on given sample information we need to compute the 90% Confidence Interval for population mean.

To compute the Confidence Interval for population mean we need to use t distribution because here the population standard deviations is unknown.

So first we have to calculate the sample mean and standard deviations of given sample as below and further Calculation of 90% Confidence Interval for population mean is given below,

The t critical value is calculated using t table or using Excel at 15 degrees of freedom.

Hope you understood.

Thank you.