Question

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 =

Answer 1

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.