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 87 drivers and 53 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.

What justifies the use of the pooled two-sample t test?

A) The similarity of the sample means suggests that the population standard deviations are likely to be similar.

B) The similarity of the sample means suggests that the population standard deviations are likely to be different.

C) The similarity of the sample standard deviations suggests that the population standard deviations are likely to be different.

D) The similarity of the sample standard deviations suggests that the population standard deviations are likely to be similar.

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   2811 ± 43      2845 ± 47    Alcohol (grams) 0.21 ± 0.11 0.38 ± 0.11

Explanation / Answer

D) The similarity of the sample standard deviations suggests that the population standard deviations are likely to be similar.

here

hence pooled std deviation Sp=(((n-1)s12+(n2-1)S22/(n1+n2-2))1/2 =44.55

and std error =sp(1/n1+1/n2)1/2 =7.7626

there fore test stat t =(X2-X1)/std error =4.38

for df =n1+n2-2 =138

hence p value for one taield test =0.0000

S1 43.000 S2 47.000 n1 87 n2 53 X1 2811.000 X2 2845.000

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