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

Driver total calories x = 2823

n = 87

sd = SE X root n = 11 X 9.33 = 102.601

Driver Alcohol: x = 0.27

n= 87

sd = SE X root n = 0.06X 9.33 = 0.559

Conductor Total calories : x = 2847

n=62

sd = se X root n = 22X 7.874 = 173.228

Conductor alcohol: x = 0.36

n=62

sd = 0.12 X 7.874 = 0.945

(b)

t = -1.058 (analysis outpput given below)

degree of freedom = 147

P = 0.291

Conclusion Do not reject the null hypothesis

Differences in alcohol consumption between driver and conductor

C t = -0.727

P = 0.467

Conclusion: Do not reject the null hypothesis (analysis output given below)

D. 95% confidence interval for mean daily alcohol consumption for London double-decker bus conductors

95% CI = 0.120 to 0.599

E. Give 99% confidence interval for the differences in the mean daily alcohol consumption for drivers and conductors

99% CI = -0.412 to 0.232

(analysis output given below)

Output of STATA

Difference between the .driver and conductor mean calories

Two-sample t test with equal variances
------------------------------------------------------------------------------
| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | 87 2823 10.99998 102.601 2801.133 2844.867
y | 62 2847 21.99998 173.228 2803.008 2890.992
---------+--------------------------------------------------------------------
combined | 149 2832.987 11.18065 136.4773 2810.892 2855.081
---------+--------------------------------------------------------------------
diff | -24 22.67365 -68.80842 20.80842
------------------------------------------------------------------------------
diff = mean(x) - mean(y) t = -1.0585
Ho: diff = 0 degrees of freedom = 147

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.1458 Pr(|T| > |t|) = 0.2916 Pr(T > t) = 0.8542

Differences betwen alcohol consumption between driver and conductor

Two-sample t test with equal variances
------------------------------------------------------------------------------
| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | 87 .27 .0599311 .559 .1508609 .3891391
y | 62 .36 .1200151 .945 .1200149 .5999851
---------+--------------------------------------------------------------------
combined | 149 .3074497 .0608458 .7427174 .1872109 .4276884
---------+--------------------------------------------------------------------
diff | -.09 .123638 -.3343376 .1543376
------------------------------------------------------------------------------
diff = mean(x) - mean(y) t = -0.7279
Ho: diff = 0 degrees of freedom = 147

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.2339 Pr(|T| > |t|) = 0.4678 Pr(T > t) = 0.7661

99% CI differnces between driver and condutor

ttesti 87 0.27 0.559 62 0.36 0.945, level(99)

Two-sample t test with equal variances
------------------------------------------------------------------------------
| Obs Mean Std. Err. Std. Dev. [99% Conf. Interval]
---------+--------------------------------------------------------------------
x | 87 .27 .0599311 .559 .1121288 .4278712
y | 62 .36 .1200151 .945 .0408969 .6791031
---------+--------------------------------------------------------------------
combined | 149 .3074497 .0608458 .7427174 .1486752 .4662241
---------+--------------------------------------------------------------------
diff | -.09 .123638 -.4126567 .2326567
------------------------------------------------------------------------------
diff = mean(x) - mean(y) t = -0.7279
Ho: diff = 0 degrees of freedom = 147

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.2339 Pr(|T| > |t|) = 0.4678 Pr(T > t) = 0.7661

.

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