AMS communicates with customers who subscribe to telecommunications services through a special secured email interface that sends messages about service changes, new features, and billing information to in-home digital set-top boxes for later display. To enhance customer service, the operations department established the business objective of reducing the amount of time to fully update each subscriber's set of messages. The department selected three candidate messaging systems and conducted an experiment in which 45 randomly chosen cable subscribers were assigned one of the three systems (15 assigned to each system). Update times were measured, and the results are organized and stored in the below Table1.

Table1. Update times (in seconds) for 3 different email systems Observation Email Email Email System 1 System 2 System 3 1 4.13 3.71 3.88 2 3.75 3.89 4.21 3 3.93 4.22 4.52 4 3.74 4.57 3.48 5 3.36 4.24 4.83 6 3.85 3.9 3.78 7 3.26 4.09 4.11 8 3.73 4.05 4.36 9 4.06 4.07 4.18 10 3.33 3.8 3.64 11 3.96 4.36 3.91 12 3.57 4.33 2.87 13 3.13 3.49 3.64 14 3.68 3.57 3.61 15 3.63 4.74 3.58 instructions: Analyze the data in Table1 performing statistical hypothesis tests for the differences in the population mean, variance, correlation, between each two independent groups of email system pairs. Use level of significance at = 0.05. Use and present answer with 4 decimals. Write a report to the operations department that indicates your findings