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 85 drivers and 63 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.

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 different.

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

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.)

Drivers Conductors Total calories   2823 ± 42     2842 ± 47   Alcohol (grams) 0.22 ± 0.03 0.36 ± 0.14

Explanation / Answer

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

Answer:

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.

Solution:

Here, we have to use pooled two sample t test for checking the given claim. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The conductors consume same calories per day as the drivers.

Alternative hypothesis: Ha: The conductors consume more calories per day than do drivers.

H0: µ1 = µ2 versus Ha: µ1 > µ2

For conductors

Sample mean = X1bar = 2842

SE = 47

N1 = 63

SE = S/sqrt(n)

S = SE*sqrt(n)

S1 = 373.05

For drivers

Sample mean = X2bar = 2823

SE = 42

N2 = 85

S2 = 387.22

Alpha = 0.05

Degrees of freedom = N1 + N2 – 2 = 146

df = 146

(X1bar – X2bar) = 19

Standard error = 63.3841(by using pooled variance)

Test statistic = t = (X1bar – X2bar) / Standard error = 19/63.3841 = 0.2998

t = 0.2998

Upper critical value = 1.6554 (By using t-table)

P-value = 0.3824 (by using t-table or excel)

Alpha = 0.05

P-value > Alpha value

So, we do not reject the null hypothesis

So, we conclude that there is insufficient evidence that the conductors consume more calories per day than do drivers.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.