A paper described a survey of 499 undergraduate students at a state university i

Question

A paper described a survey of 499 undergraduate students at a state university in the southwestern region of the United States. Each student in the sample was classified according to class standing (freshman, sophomore, junior, or senior) and body art category (body piercings only, tattoos only, both tattoos and body piercings, no body art). Use the data in the accompanying table to determine if there is evidence that there is an association between class standing and response to the body art question. Assume that it is reasonable to regard the sample of students as representative of the students at this university. Use alpha = 0.01. State the null and alternative hypotheses. H_0: The response proportions are not all the same for all class standings. H_a: The response proportions are the same for all class standings. H_0: Class standing and body art response are not independent. H_a: Class standing and body art response are independent. H_0: The response proportions are the same for all class standings. H_a: The response proportions are not all the same for a class standings. H_0: Class standing and body art response are independent. H_a: Class standing and body art response are not independent. Calculate the test statistic () What is the P-value for the test? (Round your answer to four decimal places.)

Explanation / Answer

The chi-square statistic is 29.2749. The p-value is .000582. The result is significant at p < .01.

Results A B C D Row Totals 1 63  (51.36)  [2.64] 7  (15.17)  [4.40] 16  (19.30)  [0.57] 86  (86.17)  [0.00] 172 2 45  (39.12)  [0.89] 11  (11.55)  [0.03] 10  (14.70)  [1.50] 65  (65.63)  [0.01] 131 3 20  (23.59)  [0.55] 9  (6.97)  [0.59] 7  (8.87)  [0.39] 43  (39.58)  [0.30] 79 4 21  (34.94)  [5.56] 17  (10.32)  [4.33] 23  (13.13)  [7.42] 56  (58.62)  [0.12] 117 Column Totals 149 44 56 250 499  (Grand Total)

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