Question 1 Analyzing Production Efficiency in Manufacturing Objective: To use hypothesis testing concepts to compare the production efficiency of two types of machine tools in a manufacturing plant. Background: 10 Points A manufacturing company is considering the introduction of a new type of machine tool (Machine Tool Y) to work alongside its existing machine tool (Machine Tool X). The project's goal is to assess the efficiency of the new machine tool in terms of operation time, wear rate, and variability in operation time. Data Collection: 1. Randomly select products manufactured using Machine Tool X and Machine Tool Y. 2. Record the operation time for each selected product. 3. Record the number of products showing wear from the samples. 4. Calculate the sample mean and sample standard deviation of operation time for both machine tools. Sample Data for n = 10: Product No. Machine Tool X Operation Time (mins) Machine Tool Y Operation Time (mins) Wear on X (Yes=1/No=0) 1 12 11 2 13 10 3 4 14 12 Wear on Y (Yes=1/No=0) 1 0 0 1 1 22 12 11 0 0 5 15 12 1 1 13 10 0 0 7 14 11 1 0 8 12 12 0 1 9 13 11 1 0 10 14 10 0 0