# Data 4.2 on page 223 describes an experiment to study the effects of smiling on leniency in judging students accused of cheating. Exercise 4.60 on page 250 shows a dotplot, reproduced in Figure 5.19, of a randomization distribution of differences

_{0}: Î¼

_{s}= Î¼

_{n}vs H

_{a}: Î¼

_{s}> Î¼

_{n}, where Î¼s and Î¼n are the mean leniency scores for smiling and neutral expressions, respectively. This distribution is reasonably bell-shaped and we estimate the standard error of the differences in means under the null hypothesis to be about 0.393. For the actual sample in Smiles, the original difference in the sample means is D = xÌ…

_{s}ˆ’ xÌ…

_{n}= 4.91 ˆ’ 4.12 = 0.79. Use a normal distribution to find and interpret a p-value for this test.

Figure 5.19

**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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**Transcribed Image Text:**

## -1.0 -0.5 0.0 0.5 1.0 D = 0.79 Dff

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**Related Book For**

## Statistics Unlocking The Power Of Data

**ISBN:** 9780470601877

1st Edition

**Authors:** Robin H. Lock, Patti Frazer Lock, Kari Lock Morgan, Eric F. Lock, Dennis F. Lock

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**5**- Approximating with a Distribution

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