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Chi-square statistics tests for goodness of fit and independence

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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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Solution Summary

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

Solution Preview

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 provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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