A researcher is investigating the physical characteristics t

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 woman 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 college students, and each student is asked to select the \"most beautiful\" of the three faces. The distribution of responses was as follows.

Do the data indicate any significant preferences among the three versions of the photograph? Test at the .05 level of significance. (Use 2 decimal places.)

Conclusion

a. Fail to reject the null hypothesis, there are significant preferences.

b. Fail to reject the null hypothesis, there are not significant preferences.  

c. Reject the null hypothesis, there are not significant preferences.

d. Reject the null hypothesis, there are significant preferences.

Solution

The expected values are 50, 50, 50 for each, if there are no preferences.

Using

df = a - 1 = 3 - 1 = 2,

chi^2 (critical) = 5.991464547 [ANSWER]

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Using

chi^2 = Sum[(O - E)^2 / E]

Then

chi^2 = 20.28 [ANSWER]

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Conclusion:

As chi^2 > chi^2(crit), we:

OPTION D: Reject the null hypothesis, there are significant preferences.