Question

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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 α = 0.01 Both Body Tattoos 14 10 Body No Art 86 PiercingsTattoos Piercing and Body Only Only Freshman Sophomore Junior Senior 63 20 9 17 24 56 State the null and alternative hypotheses. Ho: Class standing and body art response are independent. H: Class standing and body art response are not independent. OHo: The response proportions are not all the same for all class standings Ha: The response proportions are the same for all class standings. O Ho: The response proportions are the same for all class standings. Ha: The response proportions are not all the same for all class standings. Ho: Class standing and body art response are not independent. Ha: Class standing and body art response are independent. Calculate the test statistic. (Round your answer to two decimal places.) 31.77 What is the P-value for the test? (Round your answer to four decimal places.) P-value = 0.0001

Answer 1

applying chi square test on above data:

Expected	Ei=Σrow*Σcolumn/Σtotal	body piercing	tatoos	both	neither	Total
	freshman	50.42	14.99	18.74	85.85	170
	sophomore	38.85	11.55	14.44	66.16	131
	Junior	23.73	7.05	8.82	40.40	80
	Senior	35.00	10.40	13.01	59.59	118
	Total	148	44	55	252	499
chi square    χ2	=(Oi-Ei)2/Ei	body piercing	tatoos	both	neither	Total
	freshman	3.1380	4.2590	1.1980	0.0000	8.595
	sophomore	0.6820	0.0260	1.3650	0.0000	2.073
	Junior	0.5860	0.5370	0.3750	0.3210	1.819
	Senior	5.5990	4.1800	9.2930	0.2160	19.288
	Total	10.005	9.002	12.231	0.537	31.78

from above chi square test statistic X² =31.78