The manager of a coffee shop called Perks is interested in determining if a new ordering system that a competitor's store, Cool Beans, has been using might make service time quicker on average at his store.Minor differences in mean service time are to be expected, but a decrease of more than 30 seconds using the new systemwould be practically significant to the manager of Perks and allow him to conclude the new technology would be useful for his business.

Let₁be the mean service time at Perks and₂be the mean service time at Cool Beans.The manager goes through the point-of-sale data and randomly selectsa sample of 46 orders from the weekday 6-10 a.m. shift (Group 1) at Perks and records the service time. He offers double overtime pay to one of his employees to hang out inconspicuouslyin the Cool Beans parking lot to watch the drive-thrulane there, recording another46 service times using its ordering system(Group 2).

The mean service time (in seconds) at Perks is284.7 with a standard deviation of 25.6, while the mean service time at Cool Beans was 217.1 with a standard deviation of 25.6.

Calculate the test statistic for testing the hypothesis that the difference in mean service time between Perks and Cool Beans is more than 30 secondsto two decimal places.Take all calculations toward the answer to four (4) decimal places.

please give step by step instructions.

Thanks,