The nature conservancy has hired you to estimate the population mean of all the lengths of fully grown male killer whales living in captivity. To estimate this population mean, you select a random sample of 13 fully grown male killer whales living in captivity and record the lengths (in m) of each male killer whale. Assume that the population is approximately normally distributed. Based on your sample, follow the steps below to construct a 95% condence interval for the population mean of all lengths of fully grown male killer whales living in captivity. (If necessary, consult a list of formulas.) (a) Click on '"l'ake Sample" to see the results for your random sample. Number of killer whales Sample mean Sample standard deviation Take Sample 13 6.894 1.422 Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 95% condence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Sample size: X \\(3 I) ll . Standard error: Point estimate: III Sample standard deviation: Margin of error: Confidence level Critical value Critical value: 0 99% $0.005 = 3.055 95% confidence interval: 95% 0.025 = 2.179 Compute 90% 0.050 = 1.782 (b) Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of all the lengths of fully grown male killer whales living in captivity. 95% confidence interval: 0.000 10.000 0.000 2.000 4.000 6.000 8.000 10.000