8. One goal of the Edinburg Artery Study was to investigate the risk factors for

Question

8. One goal of the Edinburg Artery Study was to investigate the risk factors for peripheral arterial disease among persons 55 to 74 years old cholesteol levels, measured in mmol/l, among 4 populations: patients with intermittent claudication or interruptions in movement, those with major asymptomatic disease, those with minor asymptomatie disease, and those with no evidence of heart disease. The samples below were collected The LDL Population standard deviation Internittent claudication 73 Minor asymptomatic disease 105 Major asymptomatic disease 240 No disease Compute decinal values to two place accuracy. Detailed calculations not required 6.22 5.81 5.77 5.47 1.62 1.43 1.24 1.31 1080 a) Test the null hypothesis that the mean LDL leel is the same Eor all four populations. hat are the degrees of Ereedom? The degrees of freedom are df1 df2- (continued next page) Determine the following quantities: From Table A.5, the .05 significance value for dfl (numerator)-3and df2 (denominator)s n-k = 1494 is 2.60. Do you rejeet7 (Yes/No) b) Thereenough evidence to conclude that at least one of LDL levels are not equal c) What conditions must hold for this test to be valid? Answer below. d) When is it appropriate to determine which means are different? Answer below Is it appropriate for this test? (Yes/No)

Explanation / Answer

(a) Degree of freedom dF1 = 4 -1 = 3

Degree of freedom dF 2 = (73-1) + (105 -1) + (240 -1) + (1080 -1) = 1494

Grand mean xbar = (73 * 6.22 + 105 * 5.81 + 240 * 5.77 + 1080 * 5.47)/ 1498 = 5.578

sw2 = 1/(1498 - 4) * [ (73-1) * 1.622 + (105 -1) * 1.432 + (240 -1) * 1.242 + (1080 -1) * 1.312] = 2620.785/ 1494 = 1.7542

s2b = 1/3 * [ 73 * (6.22 - 5.578)2 + 105 * ( 5.81 - 5.578)2 + 240 * (5.77- 5.578)2 + 1080 * (5.47 - 5.578)2 ]

= 57.18368/3 = 19.06123

F = 19.06123/ 1.7542 = 10.866

(ii) Fcritical = F(3, 1494) = 2.60

so we will reject the null hypothesis.

(b) THere is enough evidence to conclude that at least one of LDL levels are not equal.

(c) THe follwing conditions must hold:

(d) WHen we will reject the null hypothesis and we come to know that at lease one mean is different.

Here we requre to know which mean is different from others.

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