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 94 drivers and 70 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.

(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 2824 ± 15 2840 ± 16 Alcohol (grams) 0.25 ± 0.12 0.36 ± 0.14

Explanation / Answer

Solution

Let X = daily alcohol consumption of London double-decker bus drivers and

Y = daily alcohol consumption of London double-decker bus conductors.

We assume X ~ N(µ1, 12) and Y ~ N(µ2, 22) and 1 = 2 = , say but which is unknown.

Part (a)

100(1 – ) % confidence interval for µ2 when 22 is unknown is: {Ybar ± (s/n2)(t/2)}, where

Ybar = sample mean,

1 = population standard deviation,

s1 = sample standard deviation,

n2 = sample size and

t/2 = upper (/2) % point of t-Distribution with (n2 - 1) degrees of freedom..

Given, n2 = 70, = ,0.05 Ybar = 0.36, s2 = 0.14, and t69,0.025 = 1.995, [using Excel Function],

So, 95% Confidence Interval for the mean alcohol consumption of double-decker bus conductors is:

{0.36 ± (0.14/70)(1.995)} = (0.360 ± 0.033) ANSWER

ANSWER

Part (b)

100(1 – ) % confidence interval for (1 - 2) is:

|Ybar – Xbar| ± (t/2)[s/{(1/n1) + {(1/n2)}], where

Xbar = sample mean of X,

Ybar = sample mean of Y,

s = estimate of common population standard deviation, given by s2 = {(n1 - 1)s12 + (n2 - 1)s22)/(n1 + n2 - 2) and

t/2 = upper (/2) % point of t-Distribution with (n1 + n2 - 2) degrees of freedom..

Given, n1 = 94, n2 = 70, = ,0.05, Xbar = 0.25, Ybar = 0.36, s1 = 0.12, s2 = 0.14, and t162,0.005 = 2.667, [using Excel Function],

So, 99% Confidence Interval for the difference in mean alcohol consumption of double-decker bus conductors and driversis:

(0.1 ± 0.053) ANSWER

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