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

	Blonde	Brunette	Red Head
Short and Slender	89	85	53
Short and Pudgy	70	90	69
Tall and Slender	51	117	62
Tall and Heavy	60	96	63

R vector Data: 89,70,51,60,85,90,117,96,53,69,62,63

Contigency Table

What can be concluded at the αα = 0.01 significance level?

1. What is the correct statistical test to use?
   Select an answer Homogeneity Goodness-of-Fit Independence Paired t-test  
2. What are the null and alternative hypotheses?
   H0:H0: Select an answer The distribution of hair color is not the same for each body type. The distribution of hair color is the same for each body type. Hair color and body type are dependent. Hair color and body type are independent.  
   
   
   H1:H1: Select an answer Hair color and body type are dependent. Hair color and body type are independent. The distribution of hair color is the same for each body type. The distribution of hair color is not the same for each body type.
3. The test-statistic for this data =  (Please show your answer to three decimal places.)
   
4. The p-value for this sample = (Please show your answer to four decimal places.)
   
5. The p-value is Select an answer greater than less than (or equal to)  αα  
   
6. Based on this, we should Select an answer fail to reject the null accept the null reject the null  
7. Thus, the final conclusion is... Select an answer At the 1% significance level, the data provides insufficient evidence to conclude that hair color and body type are dependent. At the 1% significance level, the data provides sufficient evidence to conclude that hair color and body type are dependent.

Answer 1

Sol:

As per the given data

Given table	Blonde	Brunette	Red Head	Total
Short & slender	89	85	53	227
Short & Pudgy	70	90	69	229
Tall & Slender	51	117	62	230
Tall & Heavy	60	96	63	219
Total	270	388	247	905

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,

P(ҳ6 15.538) 0.0165

e) Since the p-value > 0.01 the given sig