Data 4.2 on page 223 describes an experiment to study the effects of smiling on leniency in judging students accused of cheating. The full data are in Smiles. In Example 4.2 we consider hypotheses H₀: μ_s= μ_nvs H_a: μ_s> μ_nto test if the data provide evidence that average leniency score is higher for smiling students (μs) than for students with a neutral expression (μ_n). A dotplot for the difference in sample means based on 1000 random assignments of leniency scores from the original sample to smile and neutral groups is shown in Figure 4.20.

(a) The difference in sample means for the original sample is D = xÌ…_s ˆ’ xÌ…_n = 4.91 ˆ’ 4.12 = 0.79 (as shown in Figure 4.20). What is the p-value for the one-tailed test?

(b) In Example 4.3 on page 223 we consider the test with a two-tailed alternative, H₀: μ_s = μ_n vs H_a: μ_s ‰  μ_n, where we make no assumption in advance on whether smiling helps or discourages leniency. How would the randomization distribution in Figure 4.20 change for this test? How would the p-value change?  

Figure 4.20

Data 4.2 on page 223

Can a simple smile have an effect on punishment assigned following an infraction? LeFrance and Hecht conducted a study examining the effect of a smile on the leniency of disciplinary action for wrongdoers. Participants in the experiment took on the role of members of a college disciplinary panel judging students accused of cheating. For each suspect, along with a description of the offense, a picture was provided with either a smile or neutral facial expression. A leniency score was calculated based on the disciplinary decisions made by the participants. The full data can be found in Smiles. The experimenters have prior knowledge that smiling has a positive influence on people, and they are testing to see if the average lenience score is higher for smiling students than it is for students with a neutral facial expression (or, in other words, that smiling students are given more leniency and milder punishments.)

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