$3.($CPMK $3)$A machine is a physical system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems. The mean number of revolutions per minute $($RPM$)$ of two competing machines are to be compared. Thirty engines are randomly selected from each type, with the following results. Both populations have normal distribution. Use a $=0\mathrm{.}05$ to show that both machines have the same performance.Machine$1$SampleNumber of RPMPopulation Standard Deviation$702$Mean $1,5501,600$a$.$ What are the hypotheses?$80$Page $2$ of $3$b$.$ What is the confidence interval?C$.$ What is the statistics test used and reason?d$.$ What is the critical value table for the distribution?e$.$ What is the decision rule?True Knowledge, Faith in Christ