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 54 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 plusminus (se)." Some of the study results appear below. Give x and s for each of the four sets of measurements. (Give answers accurate to 3 decimal places.) Drivers Total Calories: x = 2828 s = Drivers Alcohol: x = s = Conductors Total Calories: x = s = Conductors Alcohol: x = s = 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.) t = df = Conclusion Reject H_o. Do not reject H_o.

Explanation / Answer

a)

Using the table:

Drivers total calories: X = 2828
s = 9

Drivers Alcohol: X = 0.22
s = 0.05

Conductors Total Calories: X = 2849
s = 10

Conductors Alcohol: X = 0.43
s = 0.12 [ANSWERS]

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    2849          
X2 =    2828          
              
Calculating the standard deviations of each group,              
              
s1 =    10          
s2 =    9          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    54          
n2 = sample size of group 2 =    86          

Also, sD =    1.671440192          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    12.56401521   [ANSWER]

As conductors are fewer,

df = n1 - 1 = 53 [ANSWER]

Getting the P value,

P = 8.03082E-18

As P < 0.05, we REJECT HO. [ANSWER]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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