To determine if there is a relationship between skin color and beauty judgements, one researcher conducted a study with a random sample of 300 black women. They were given three pictures of super models with varying skin tones: Dark (Nyakim Gatwech), Medium (Adriana Lima), and Light (Natalia Vodianova). Each woman was asked to rank them from most to least beautiful. Here are the results:

	Dark Skin	Medium Skin	Light Skin
1st	55	45	35
2nd	10	45	50
3rd	40	15	5

Question 4 of 7

Question 4

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What is the expected count of women who ranked the dark skinned model as being the most beautiful (ranked as #1)?

35

47.25

135

300

85

Question 5 of 7

Question 5

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The count that you found in the previous question is the number of women who would rank the model with the dark skin as the most beautiful that you would expect to see assuming that:

the conditions that allow us to safely use the chi-squared procedure are met

skin color and beauty perception are related

skin color and beauty perception are independent

the null hypothesis of the chi-squared test for independence in this case is true

Both C and D are correct

Question 6 of 7

Question 6

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The following is the (edited) output of the chi-squared test in this case:

The chi-square statistic is 62.6071. The p-value is < 0.00001.

the data do not provide sufficient evidence to conclude that skin color and beauty preferences are related.

the data do not provide sufficient evidence to conclude that skin color and beauty preferences are independent.

the data provide sufficient evidence to conclude that skin color and beauty preferences are related.

the data provide sufficient evidence to conclude that skin color and beauty preferences are independent.

Question 7 of 7

Question 7

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Which of the following facts should make you the most worried about the reliability of the results of the test in this case?

There is no need to worry because all of the expected cell counts are above 5.

The sample was only 300 black women and is not representative of all black women.

Two of the six observed counts are 5 or less.

Not all of the cells' contributions to the chi-squared statistic are greater than 1.

Two of the six expected counts are less than 5.