Wait staff at restaurants have employed various strategies to increase tips. An article...

Wait staff at restaurants have employed various strategies to increase tips. An article in the Sept. 5, 2005, New Yorker reported that “In one study a waitress received 50% more in tips when she introduced herself by name than when she didn’t.” Consider the following (fictitious) data on tip amount as a percentage of the bill:

Does this data suggest that an introduction increases tips on average by more than 50%? State and test the relevant hypotheses. [Hint: Consider the parameter θ = μ₁ – 1.5μ₂ ]