Do various occupational groups differ in their diets? A British study of this qu
ID: 3207530 • Letter: D
Question
Do various occupational groups differ in their diets? A British study of this question compared 95 drivers and 65 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 = 0.29
s = 0.877
Conductors Total Calories: x =
s =
Conductors Alcohol: x =
s = 1.048
(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.)
(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
(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.)
( , )
Explanation / Answer
Result:
Do various occupational groups differ in their diets? A British study of this question compared 95 drivers and 65 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.
Drivers
Conductors
Total calories
2826 ± 15
2840 ± 15
Alcohol (grams)
0.29 ± 0.09
0.38 ± 0.13
(a) Give x and s for each of the four sets of measurements. (Give answers accurate to 3 decimal places.)
Drivers Total Calories: x = 2826 s = 146.202
Drivers Alcohol: x = 0.29 s = 0.877
Conductors Total Calories: x = 2840 s =120.934
Conductors Alcohol: x = 0.38 s = 1.048
(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.)
t =1.669
df =64
There is no significant evidence at the 5% level that conductors consume more calories per day than do drivers.
Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
65
Sample Mean
2840
Sample Standard Deviation
120.9340
Population 2 Sample
Sample Size
95
Sample Mean
2826
Sample Standard Deviation
146.2020
Degrees of Freedom
64
Standard Error
21.2132
Difference in Sample Means
14.0000
t Test Statistic
0.6600
Upper-Tail Test
Upper Critical Value
1.6690
p-Value
0.2558
Do not reject the null hypothesis
(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 = 0.569
Conclusion: there is no significant is the observed difference in mean alcohol consumption.
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
65
Sample Mean
0.38
Sample Standard Deviation
1.0480
Population 2 Sample
Sample Size
95
Sample Mean
0.29
Sample Standard Deviation
0.8770
Intermediate Calculations
Degrees of Freedom
64
Standard Error
0.1581
Difference in Sample Means
0.0900
Separate-Variance t Test Statistic
0.5693
Two-Tail Test
Lower Critical Value
-1.9798
Upper Critical Value
1.9798
p-Value
0.5702
Do not reject the null hypothesis
(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.)
( , )
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
1.048
Sample Mean
0.38
Sample Size
65
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.129988402
Degrees of Freedom
64
t Value
1.9977
Interval Half Width
0.2597
Confidence Interval
Interval Lower Limit
0.120
Interval Upper Limit
0.640
(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.)
( , )
Population 1 Sample Degrees of Freedom
64
Population 2 Sample Degrees of Freedom
94
Total Degrees of Freedom
158
Pooled Variance
0.9025
Standard Error
0.1529
Difference in Sample Means
0.0900
Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level
99%
Intermediate Calculations
Degrees of Freedom
158
t Value
2.6073
Interval Half Width
0.3987
Confidence Interval
Interval Lower Limit
-0.309
Interval Upper Limit
0.489
Drivers
Conductors
Total calories
2826 ± 15
2840 ± 15
Alcohol (grams)
0.29 ± 0.09
0.38 ± 0.13
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