Do various occupational groups differ in their diets? A British study of this qu

Question

Do various occupational groups differ in their diets? A British study of this question compared 86 drivers and 51 conductors of London double-decker buses. The conductors' jobs require more physical activity. The article reporting the study gives the data as "Mean daily consumption ± (se)." Some of the study results appear below.

Is there significant evidence at the 5% level that conductors consume more calories per day than do drivers? Use the pooled two-sample t test to obtain the P-value. (Give answers to 3 decimal places.)

t =

df =

P-value =

Drivers Conductors Total calories 2812 ± 40 2840 ± 50 Alcohol (grams) 0.21 ± 0.05 0.36 ± 0.08

Explanation / Answer

Data:      

n1 = 86     

n2 = 51     

x1-bar = 2812     

x2-bar = 2840     

s1 = 40 * 86 = 370.94     

s2 = 50 * 51 = 357.07     

Hypotheses:      

Ho: 1 2      

Ha: 1 < 2      

Decision Rule:      

= 0.05     

Degrees of freedom =   86 + 51 - 2 = 135   

Critical t- score =   -1.656219133    

Reject Ho if t <   -1.656219133    

Test Statistic:      

Pooled SD, s = [{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =      (((86 - 1) * 370.94^2 + (51 - 1) * 357.07^2) / (86 + 51 - 2)) = 365.8642771

SE = s * Ö{(1 /n1) + (1 /n2)} = 365.864277111973 * ((1/86) + (1/51)) = 64.66153008    

t = (x1-bar -x2-bar)/SE = (2812 - 2840)/64.6615300801475 = -0.433024087    

p- value = 0.332844157    

Decision (in terms of the hypotheses):      

Since -0.433024087 > -1.656219133 we fail to reject Ho

Conclusion (in terms of the problem):      

There is no sufficient evidence that conductors consume more calories than drivers.      

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