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 62 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.

(a) Give x and s for each of the four sets of measurements. (Give answers accurate to 3 decimal places.)
Drivers Total Calories: x = ____________
s = ___________
Drivers Alcohol: x = __________
s = ___________
Conductors Total Calories: x = __________
s = ___________
Conductors Alcohol: x = ___________
s = _____________

(b) Is there significant evidence at the 5% level that conductors consume more calories per day than do drivers? Use the conservative two-sample t method to find the t-statistic, and the degrees of freedom. (Round your answer for t to three decimal places.)

Conclusion:

___ Reject H0

___ Do not reject H0.   

(c) How significant is the observed difference in mean alcohol consumption? Use the conservative two-sample t method to obtain the t-statistic. (Round your answer to three decimal places.)
t = _________

Conclusion:

____Reject H0

_____Do not reject H0.     

(d) Give a 95% confidence interval for the mean daily alcohol consumption of London double-decker bus conductors. (Round your answers to three decimal places.)
(________ , __________ )

(e) Give a 99% confidence interval for the difference in mean daily alcohol consumption for drivers and conductors. (conductors minus drivers. Round your answers to three decimal places.)
( _______ , __________ )

Drivers Conductors Total calories 2823 ± 11 2847 ± 22 Alcohol (grams) 0.27 ± 0.06 0.36 ± 0.12

Explanation / Answer

(A)
sample size of drivers, n1 = 87
sample size of conductors, n2 = 62

SE = s/sqrt(n)
s = SE*sqrt(n)

Drivers total calories: x = 2823, s=11/sqrt(87) = 1.1793
Drivers Alcohol: x = 0.27, s=0.06/sqrt(87) = 0.0064
Conductors Total calories: x = 2847, s=22/sqrt(62) = 2.794
Conductors Alcohol: x = 0.36, s=0.12/sqrt(62) = 0.0152

(B)

p-value = 0.000

As p-value is less than significance level 0.05, we reject the null hypothesis. This means there is significant evidence that conductors' consumption of calaroies is more than driver.

x1(bar) 2823 x2(bar) 2847 s1 1.1793 s2 2.794 n1 87 n2 62 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 0.0160 (s22/n2) 0.1259 SE 0.38 DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } [ (s12 / n1)2 / (n1 - 1) ] 0.000003 [ (s22 / n2)2 / (n2 - 1) ] 0.000260 (s12/n1 + s22/n2)2 0.020134 DF = 77

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