The newest model of a car battery from a popular brand is supposed to have a lifetime of 60 months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes of this model of car battery is approximately normally distributed. A consumer report claims that the standard deviation of this population is 0.86 months. You are a product reviewer who wants to test this claim with a random sample of 26 car batteries. Based on your sample, follow the steps below to construct a 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. Then state whether the confidence interval you construct contradicts the report's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from the random sample. Take Sample Number of car batteries 26 Sample mean Sample standard deviation Sample variance 59.94 0.48 0.2304 To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your 99% confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute". Point estimate of the population variance: ☐ Sample size: 99% confidence interval for the population variance: Critical values Left critical value: Left Right X0.995 10.52 0.005-46.928 Right critical value: 99% confidence interval for the population standard deviation: X0.975 =13.12 0.025 =40.646 Compute = X0.950 14.611.050 -37.652 (b) Based on your sample, graph the 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. • Enter the values for the lower and upper limits on the graph to show your confidence interval. Round the values to two decimal places. • For the point (*) enter the claim 0.86 from the report on your graph. (c) 0.00 0.00 99% confidence interval for the population standard deviation: 0.50 1.00 1.00 Does the 99% confidence interval you constructed contradict the report's claim? Choose the best answer from the choices below. No, the confidence interval does not contradict the claim. The claimed standard deviation 0.86 is inside the 99% confidence interval. No, the confidence interval does not contradict the claim. The claimed standard deviation 0.86 is outside the 99% confidence interval. Yes, the confidence interval contradicts the claim. The claimed standard deviation 0.86 is inside the 99% confidence interval. ○ Yes, the confidence interval contradicts the claim. The claimed standard deviation 0.86 is outside the 99% confidence interval.