Question

In: Advanced Math

Do various occupational groups differ in their diets? A British study of this question compared 85...

Do various occupational groups differ in their diets? A British study of this question compared 85 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 2820 ± 42 2840 ± 48 Alcohol (grams) 0.23 ± 0.09 0.44 ± 0.05 What justifies the use of the pooled two-sample t test? The similarity of the sample standard deviations suggests that the population standard deviations are likely to be similar. The similarity of the sample means suggests that the population standard deviations are likely to be different. The similarity of the sample means suggests that the population standard deviations are likely to be similar. The similarity of the sample standard deviations suggests that the population standard deviations are likely to be different. 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 =

Solutions

Expert Solution

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

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

b) Summary data

Drivers Conductors
Sample size 85 65
Mean Calories 2820 2840
Std Error 42 48
Std. Dev 387.22 386.99

Std.Dev = Std.error*sqrt(n)

Two-Sample T-Test and CI

Method

μ₁: mean of Drivers
µ₂: mean of Conductors
Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample N Mean StDev SE
Mean
Sample 1 85 2820 387 42
Sample 2 65 2840 387 48

Estimation for Difference

Difference Pooled
StDev
95% Upper Bound
for Difference
-20.0 387.1 85.6

Test

Null hypothesis H₀: μ₁ - µ₂ = 0
Alternative hypothesis H₁: μ₁ - µ₂ < 0
T-Value DF P-Value
-0.314 148 0.377

since p-value is more than 0.05 we fail to reject null hypothesis, there is no significant evidence to conclude that conductors consume more calories per day than do drivers.


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