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Chi-square statistics tests for goodness of fit and independence

A researcher is investigating the physical characteristics that influence whether a person's face is judged as beautiful. The researcher selects a photograph of a women and then creates two modifications of the photo by (1) moving the eyes slightly farther apart and (2) moving the eyes slightly closer together. The original photograph and the two modifications are then shown to a sample of n=150 collage students, and each student is asked to select the "most beautiful: of the three faces. The distribution of responses was as follows:

Original Eyes moved Eyes moved
Photo Apart Together
51 72 27

Do the data indicate any significant preferences among the three versions of the photograph? Test this at the .05 level of significance.

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H0: there is no significant preferences among the three versions of the photograph;
Ha: there is a significant preference among the three versions of the photograph.

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Solution Summary

This response tests for significant preferences among distribution responses at a 0.5 level of significance.