This data set, "Beer Goggles", provides median attractiveness ratings of 50 attractive or unattractive faces after consuming different amounts of alcohol. Variables: FaceType Attractiveness of the rated faces based on facial symmetry ('0' = unattractive, '1' = attractive). Alcohol Amount of alcohol consumed ('0' = Placebo group with 500 ml of non-alcoholic beer, '1' = Low-dose group with 500 ml of average strength beer (4% ABV), '2' = High-dose group with 500 ml of strong beer (7% ABV). Attractiveness Median of the 50 attractiveness ratings on a scale from 0 ("pass me a paper bag") to 10 ("pass me their phone number"). Reference: Field, A. (2017). Discovering statistics using IBM SPSS statistics (5th ed.). London: SAGE.

We have no reason to assume that the distribution of attractiveness scores is approximately normal. Assuming so when that is not the case is problematic.

Answer the following

The central limit theorem only applies under some circumstances. Determine if it is appropriate to apply the central limit theorem to the attractiveness scores. Explain your reasoning.