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 89 drivers and 67 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 2827 ± 12 2850 ± 22 Alcohol (grams) 0.26 ± 0.1 0.39 ± 0.14 (a) Give x and s for each of the four sets of measurements. (Give answers accurate to 3 decimal places.) Drivers Total Calories: x Drivers Alcohol: x= Conductors Total Calories: x = | S- Conductors Alcohol: x- (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.) df- Conclusion O Reject Ho Do not reject Ho (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.) Conclusion Reject Ho O Do not reject Ho

Explanation / Answer

"se" stands for standard error,defined as s/n, where n is the sample size

(a) Drivers total calories: x_bar = 2827

s = 12 x 89 = 113.208

Drivers Alcohol: x_bar = 0.26

s = 0.1 x 89 = 0.943

Conductors total calories: x_bar = 2850

s = 22 x 67 = 180.078

Conductors Alcohol: x_bar = 0.39

s = 0.14 x 67 = 1.146

(b) Null Hypothesis, H0: xCc = xCd

Alternate Hypothesis, Ha: xCc xCd

Degrees of freedom, using the conservative approach = smaller of 89-1 and 67-1 = 66

test statistic = (2850-2827) / sqrt ( 113.2082 / 88 + 180.0782 / 66 ) = 23 / 25.2383 = 0.9113

t0.95,66 = 1.668

test statistic < tcrit , so we do not have evidence to refute the nullhypothesis. There is not statistically significant difference at 5% level that conductors consume more calories per day than drivers.

Conclusion: do not reject H0

(c) Null Hypothesis, H0: xAc = xAd

Alternate Hypothesis, Ha: xAc xAd

test statistic = (0.39-0.26) / sqrt ( 0.9432 / 88 + 1.1462 / 66 ) = 0.13 / 0.1732 = 0.7505

t0.95,66 = 1.668

test statistic < tcrit , we do not have evidence to refute the nullhypothesis. There is not statistically significant difference in the mean consumption of alcohol between conductors and drivers at 5% level t.

Conclusion: do not reject H0

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

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