Question

A paper described a survey of 497 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 -0.01. Piercings Tattoos Piercing and State the null and alternative hypotheses. Ho: Class standing and body art response are not independent. Ha: Class standing and body art response are independent. Ho: The response proportions are not all the same for all class standings. Ha: The response proportions are the same for all class standings. Ho: The response proportions are the same for all class standings. He: The response proportions are not all the same for all class standings. O Ho: Class standing and body art response are independent. Ha: Class standing and body art response are not independent. Calculate the test statistic. (Round your answer to two decimal places.) What is the p-value for the test? (Round your answer to four decimal places.) P-value = What can you conclude? Do not reject Ho. There is not enough evidence to conclude that the proportions falling into the body art response categories are not all the same for the four class standings. Do not reject Ho. There is not enough evidence to conclude that there is an association between class standing and response to the body art question. Reject Ho. There is convincing evidence to conclude that there is an association between class standing and response to the body art question. Reject Ho. There is convincing evidence to conclude that the proportions falling into the body art response categories are not all the same for the four class standings.

Answer 1

Ans:

H0:class attending and body art response are independent.

H_a:class attending and body art response are not independent

	Observed(fo)
	body piercing	Tattoos	both	None	Total
Freshman	61	7	16	86	170
sophomore	45	11	10	64	130
junior	20	9	7	43	79
senior	21	17	24	56	118
Total	147	44	57	249	497
	Expected(fe)
	body piercing	Tattoos	both	None	Total
Freshman	50.28	15.05	19.50	85.17	170
sophomore	38.45	11.51	14.91	65.13	130
junior	23.37	6.99	9.06	39.58	79
senior	34.90	10.45	13.53	59.12	118
Total	147	44		249	440
	Chi square=(fo-fe)^2/fe
	body piercing	Tattoos	both	None	Total
Freshman	2.285	4.306	0.627	0.008	7.226
sophomore	1.116	0.023	1.617	0.020	2.774
junior	0.485	0.575	0.469	0.296	1.824
senior	5.537	4.111	8.095	0.165	17.908
Total	9.422	9.015	10.808	0.488	29.733

Test statistic:

chi square=29.73

df=(4-1)*(4-1)=9

p-value=CHIDIST(29.733,9)=0.0005

Reject H0.There is convincing evidence to conclude that there is an association between class attending and response to the body art question.