Question

Is there an association between hair color and body type? The table below shows the results of a researcher's observations of randomly selected people. Frequencies of Hair Colors for Various Body Types Red Blonde Brunette Head Short and 81 Slender 50 Short and 91 99 Pudgy Tall and 60 117 Slender Tall and 55 106 Heavy What can be concluded at the -0.01 significance level? 99 a. What is the correct statistical test to use? Paired t-test Goodness-of-Fit Independence Homogeneity b. What are the null and alternative hypotheses? HO: Hair color and body type are independent. The distribution of hair color is not the same for each body type. Hair color and body type are dependent. The distribution of hair color is the same for each body type. The distribution of hair color is the same for each body type. Hair color and body type are Independent. Hair color and body type are dependent. The distribution of hair color is not the same for each body type. c. The test-statistic for this data- (Please show your answer to three decimal places.) d. The p-value for this sample (Please show your answer to four decimal places.) e. The p-value is Select an answer

Answer 1

As per the given data

Given table	Blonde	Brunette	Red Head	Total
Short & slender	81	99	50	230
Short & Pudgy	91	99	79	269
Tall & Slender	60	117	62	239
Tall & Heavy	55	106	61	222
Total	287	421	252	960

deta them or not. a In the problem we have given on hair colour and body type. our task is to test for, is there any association among here, we need to test this by Chi-square test for independence. Coption e) b) The hypothesis are, Ho! hair color if body type are independent Coption ) Hii Hair color & body type are dependent l option e) c) Test statistic, 2 3 4 T-3 ] (fi; - frio fe;) n fotos vX 6 where, füj a frequency of (a)th obs. fio- ith Column sum 1,2,3 toja ith sun 11,2,3 3,4, by Calculation we get, 15. 538

Calculation for test statistic	Blonde	Brunette	Red Head	Total
Short & slender	2.179	0.034	1.783	3.996
Short & Pudgy	1.392	3.050	0.996	5.438
Tall & Slender	1.835	1.417	0.009	3.261
Tall & Heavy	1.947	0.767	0.127	2.842
Total	7.353	5.269	2.915	15.538

d) Since our test statistic will follow chi-square distribution with 6 df then the p-value will be,

PX6 > 15.538) = 0.0165

e) Since the p-value > 0.01 the given significance level, we fail to reject H0 and can comment that the hair color and body type are independent.