Are hair color and body type independent? The table below shows the results of a

Question

Are hair color and body type independent? The table below shows the results of a researcher's observations of randomly selected people.

What can be concluded at the 0.05 level of significance?

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The p-value is:

p-Value =                            [ Select ]                       ["0.21", "0.05", "0.24", "0.01"]          

Conclusion:

                           [ Select ]                       ["There is sufficient evidence to make a conclusion on whether hair color and body type are independent or dependent.", "There is insufficient evidence to make a conclusion on whether hair color and body type are independent or dependent."]      

Blonde Brunette Red Head Short and Slender 53 127 31 Short and Pudgy 62 134 36 Tall and Slender 71 118 40 Tall and Heavy 46 100 42

Explanation / Answer

We use the chi square test of independence here.

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 860

The Hypothesis:

H0: There is no relation between hair color and body type i.e they are independent.

Ha: There is a relation between hair color and body type, i.e they are dependent.

The Test Statistic: The table below gives the calculation of 2.

2test = 7.973

The Critical Value:   The critical value at = 0.05 , degrees of freedom = (r – 1) * (c -1) = ( 4 - 1) * ( 3 - 1) = 6

2critical = 12.59

The p-value:   The p value at 2 = 7.973 for df = 6

2critical = 0.24 and the range of the p value is 0.05 < p value < 0.21

The Decision Rule: If 2 test is > 2 critical, then Reject H0.

Also if p value is < , Then Reject H0.

The Decision:    Since If 2 test (7.973) is < 2 critical (12.59), We Fail to reject H0.

Also the p value (0.24) is > (0.05). Hence we Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that hair color and body type are dependent.

Observed Blonde Brunette Red Head Total Short and Slender 53 127 31 211 Short and Pudgy 62 134 36 232 Tall and Slender 71 118 40 229 Tall and Heavy 46 100 42 188 Total 232 479 149 860 Expected Blonde Brunette Red Head Total Short and Slender 56.92 117.52 36.56 211 Short and Pudgy 62.59 129.22 40.20 232 Tall and Slender 61.78 127.55 39.68 229 Tall and Heavy 50.72 104.71 32.57 188 Total 232 479 149 860

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