### Testing Battery Lifetimes of Cell PhonesA cell phone manufacturer tests the battery lifetimes of its cell phones by recording the time it takes for the battery to run out while testers are playing games on the phones continuously. The manufacturer claims that the population mean of the battery lifetimes for all phones of their latest model is 5.64 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.### Steps to Construct a 90% Confidence IntervalBased 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.#### Sample Data- **Number of phones:** 45- **Sample mean:** 5.76 hours- **Sample standard deviation:** 2.42 hours- **Population standard deviation:** 2.73 hours### Step-by-Step Instructions1. **Define the Sample Parameters:** - Sample size: 45 - Point estimate: 5.76 - Population standard deviation: 2.73 - Critical value: Choose from provided table (e.g., \( z_{0.050} = 1.645 \) for 90% confidence interval)2. **Compute the Standard Error** and **Margin of Error:** - Use formulas for standard error and margin of error based on the sample data and chosen critical value.3. **Calculate the Confidence Interval:** - Compute the lower and upper limits using the point estimate ± margin of error.4. **Graphical Representation:** - Display the computed confidence interval on a number line. - Mark the manufacturer’s claim of 5.64 hours on the graph.### Evaluating the Manufacturer’s Claim#### Question:Does the 90% confidence interval you constructed contradict the manufacturer’s claim?- **Options:** - No, the confidence interval does not contradict the claim. The manufacturer's claim of 5.64 hours is inside the 90% confidence interval. - Yes, the confidence interval contradicts the claim.

The provided information is as follows:The sample size is .The sample mean is .The sample standard…

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 5.64 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) (c) Take Sample Sample size: Point estimate: 0 Population standard deviation: 0 Critical value: 0 Compute 0.00 Number of phones 0.00 45 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". 2.00 Sample mean Standard error: Margin of error: • Enter the lower and upper limits on the graph to show your confidence interval. . For the point (◆), enter the manufacturer's claim of 5.64 hours. 4.00 5.76 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 2.42 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 10.00 O No, the confidence interval does not contradict the claim. The manufacturer's claim of 5.64 hours is outside the 90% confidence interval. Population standard O Yes, the confidence interval contradicts the claim. The manufacturer's claim of 5.64 hours is inside the 90% confidence interval. deviation Does the 90% confidence interval you constructed contradict the manufacturer's claim? Choose the best answer from the choices below. O No, the confidence interval does not contradict the claim. The manufacturer's claim of 5.64 hours is inside the 90% confidence interval. Yes, the confidence interval contradicts the claim. The manufacturer's claim of 5.64 hours is outside the 90% 2.73