Objective: To use hypothesis testing concepts to compare the production efficiency of two types of machine tools in a manufacturing plant.Background: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$\mathrm{.}2.$ Record the operation time for each selected product$\mathrm{.}3.$ Record the number of products showing wear from the samples$\mathrm{.}4.$ Calculate the sample mean and sample standard deviation of operation time for both machine tools.Sample Data for n $=10$ :TableHypothesis Testing:$1.$ Population Mean $($Operation Time$)$: a$.$ Compare the average operation time between Machine Tool X and Machine Tool Y$.$ b$.$ Perform a two$-$sample t$-$test to test if there is a significant difference in average operation time. $2.$ Population Proportion $($Wear Rate$)$: a$.$ Compare the wear rates between Machine Tool X and Machine Tool Y$.$ b$.$ Perform a two$-$sample z$-$test to test if there is a significant difference in wear rates. $3.$ Population Standard Deviation $($Variability in Operation Time$)$: a$.$ Compare the variability in operation time between Machine Tool X and Machine Tool Y$.$ b$.$ Perform an F$-$test to test if there is a significant difference in the variability of operation time.Analysis and Conclusion:$1.$ Analyze the results of the hypothesis tests for each population parameter $($mean$,$ proportion, and standard deviation$)\mathrm{.}2.$ Determine if the new machine tool $($Machine Tool Y$)$ is more efficient than the existing machine tool $($Machine Tool X$)$ based on the results$\mathrm{.}3.$ Provide recommendations for the company on whether to continue using both machine tools, replace Machine Tool X with Machine Tool Y$,$ or implement further enhancements based on the findings.