A cell phone manufacturer tests the battery lifetimes of its cell phones by recording the time it takes for the battery charges to run out while testers are playing games on the phones continuously. The manufacturer claims that the population mean of the battery lifetimes of all phones of their latest model is 5.28 hours. As a researcher for a consumer information service, you want to test that claim. To do so, you select a random sample of 45 cell phones of the manufacturer's latest model and record their battery lifetimes. Assume it is known that the population standard deviation of the battery lifetimes for that cell phone model is 2.73 hours. Based on your sample, follow the steps below to construct a 90% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. Then state whether the confidence interval you construct contradicts the manufacturer's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 45 phones of the manufacturer's latest model. (b) Take Sample Sample size: Point estimate: 0 Population standard deviation: 0 Critical value: 0 Compute 0.00 Number of phones 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 90% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". 0.00 45 2.00 Sample mean Standard error: • Enter the lower and upper limits on the graph to show your confidence interval. . For the point (◆), enter the manufacturer's claim of 5.28 hours. 4.00 6.98 Margin of error: 90% confidence interval: Based on your sample, graph the 90% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. 90% confidence interval: 5.00 6.00 Sample standard deviation 2.64 8.00 X Critical values 20.005 = 2.576 ²0.010 = 2.326 ²0.025 = 1.960 20.050 = 1.645 ²0.100 = 1.282 10.00 Population standard 10.00 deviation 2.73