An agriculture publication claims that the population mean of the birth weights for all goats is 2.81 kg. A veterinary service has hired you to test that claim. To do so, you select a random sample of 35 goats and record the birth weights. Assume it is known that the population standard deviation of the birth weights of goats is 1.36 kg. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the birth weights for all goats. Then state whether the confidence interval you construct contradicts the publication's claim. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from your random sample of 35 goats. Take Sample Number of goats Sample mean Sample standard deviation Population standard deviation 1.36 Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 99% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Critical values =z0.0052.576 =z0.0102.326 =z0.0251.960 =z0.0501.645 =z0.1001.282 ___Sample size: ___Point estimate: ___Population standard deviation: ___Critical value: Compute Standard error: Margin error: 99% confidence interval: b)Based on your sample, graph the 99% confidence interval for the population mean of the birth weights for all goats. Enter the lower and upper limits on the graph to show your confidence interval. For the point (*), enter the publication's claim of 2.81 kg. 99% confidence interval: 0.00*5.0010.00 0 2 4 6 8 10 c)Does the 99% confidence interval you constructed contradict the publication's claim? Choose the best answer from the choices below. No, the confidence interval does not contradict the claim. The publication's claim of 2.81 kg is inside the 99% confidence interval. No, the confidence interval does not contradict the