10 People tend to be more generous after receiving good news

10. 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 25 patrons of a restaurant with a message on their bill warning them that tomorrow\'s weather will be bad, the average percent tip the 25 patron left was 17% with standard deviation 4%. Suppose that percentage tips are Normal with mean . Is there good evidence that the mean percentage tip is less than 20 (at 0.05 significance level)? 1) Which test do you use?

Solution

1) We use a T TEST, as n < 30.

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Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   20  
Ha:    u   <   20   [ANSWER, HYPOTHESES]

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As we can see, this is a    left   tailed test.      
          
Getting the test statistic, as              
              
X = sample mean =    17          
uo = hypothesized mean =    20          
n = sample size =    25          
s = standard deviation =    4          
              
Thus, t = (X - uo) * sqrt(n) / s =    -3.75   [ANSWER, TEST STATISTIC]      
              
Also, the p value is, as df = n - 1 = 24,              
              
p =    0.00049427 [ANSWER, P VALUE]

As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that people are less generous when they hear bad news. [CONCLUSION]