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A gym wanted to test the effect of offering one free personal training session on customer satisfaction so their customer experience team ran an experiment. Starting on Jan 1, the gym randomly assigned 500 customers to receive the offer in January (the treatment group) and 500 customers to not receive the offer (the control group). 350 of the customers in the treatment group completed the personal training session during January. The team then measures customer satisfaction of the 350 customers who completed a free personal training session. These customers had an average customer satisfaction of 8.4 out of 10 (1 = extremely dissatisfied and 10 = extremely satisfied). They also measured customer satisfaction among the customers in the control group and they had an average customer satisfaction of 7.0 (out of 10). A t-test revealed that the 8.4 rating was significantly higher than the 7.0 rating, so the customer experience team concludes that offering a free personal training session improves customer satisfaction and decides to implement the program more broadly.
Describe the mistake that the team made in their interpretation of the results of the experiment and why it is a mistake. Then describe what (correct) analysis and calculations they should have done to determine the causal relationship between their offer and customer satisfaction.
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