22.39 Bad weather, bad tip? People tend to be more generous after receiving good news. Are they less generous after receiving bad news? The average tip left by adult Americans is 20%. Give 20 patrons of a restaurant a message on their bill warning them that tomorrow’s weather will be bad and record the tip percentage they leave. Here are the tips as a percentage of the total bill:

18.0 19.1 19.2 18.8 18.4 19.0

18.5 16.1 16.8 18.2 14.0 17.0

13.6 17.5 20.0 20.2 18.8 18.0

23.2 19.4

Suppose that tip percentages are Normal with σ = 2, and assume that the patrons in this study are a random sample of all patrons of this restaurant. Is there good evidence that the mean tip percentage for all patrons of this restaurant is less than 20 when they receive a message warning them that tomorrow’s weather will be bad? State H₀ and H_a and carry out a significance test. Use significance level 0.05.