Scientists came up with a clever way to test whether the physical act of smiling increases positive emotions. They randomly divided participants into two groups of 24 each. The ‘‘smiling” group was asked to hold a pencil between their teeth (which forces the face into a smile), while the ‘‘non-smiling” group was asked to hold a pencil between their lips (which does not). Participants were not told the purpose of the experiment. They then rated video clips on a scale from −9 (very negative) to +9 (very positive). The ratings of the two groups did not differ on the negative clips, but the mean for the smiling group on a positive clip (from a Tom & Jerry cartoon) was 7.8 while it was 5.9 for the non-smiling group.

(a) Is this an experiment or an observational study?

(b) Why is it important that participants were not told the purpose of the study?

(c) Find the difference in means for the ratings on the positive clip, and use notation, with subscripts and a minus sign, for your answer.

(d) If the difference in means from part (c) is considered substantial, can we conclude that forcing the facial muscles into a smile in this way increases positive emotions?