Q2) Chi-Square Text for Goodness of Fit (11 points) A researcher was interested
ID: 3047968 • Letter: Q
Question
Q2) Chi-Square Text for Goodness of Fit (11 points)
A researcher was interested in studying the phenomenon of social distance, which involves one’s reluctance to have social contact with members of another racial or ethnic group. The researcher set up an experiment with a group of college students in a large lecture class. The students were asked to choose a teaching assistant (TA) for their weekly break-out group in the class, and the only information they had was the last name of the TA. Here are the numbers of students who selected each TA: Chang = 15, Peterson = 32, Hernandez = 13. Conduct a Chi-square test for goodness of fit with an alpha level of .10 to answer this research question.
What is the variable in this test? What type of variable is it (nominal, ordinal, or continuous)?
Explanation / Answer
The total number of students = 15 + 32 + 13 = 60. Therefore each expected value = 60/3 = 20
The Hypothesis:
H0: There is no reluctance among students to have social contact with members of another racial or ethnic group i.e The Observed and expected values are equal (p1 = p2 = p3)
Ha: There is a reluctance among students to have social contact with members of another racial or ethnic group i.e The Observed and expected values are not equal.
The Test Statistic: The table below gives the calculation of 2.
2test = 1.25 + 7.2 + 2.45 = 10.9
The Critical Value: The critical value at = 0.1, df = (3 - 1) = 2
2critical = 4.60
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test (10.9) is > 2 critical (4.6), We Reject H0.
The Conclusion: There is sufficient evidence at the 90% significance level to conclude that there is a reluctance among students to have social contact with members of another racial or ethnic group.
The variable is the TA of different etnicities, and is a nominal variable.
Observed 15 32 13 Expected 20 20 20 O-E -5 12 -7 (O-E)2 25 144 49 (O-E)2/E 1.25 7.2 2.45Related Questions
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