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 95 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 plusminus (se)." Some of the study results appear below. (a) Give bar x and s for each of the four sets of measurements. (Give answers accurate to 3 decimal places.) Drivers Total Calories: bar x = s = Drivers Alcohol: bar x = s = Conductors Total Calories: bar x = s = Conductors Alcohol: bar x = s = (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.) t = df = Conclusion Reject H_0. Do not reject H_0. (c) How significant is the observed difference in mean alcohol consumption? Use the conservative two-sample t method to obtain the t-statistic. t = Conclusion Reject H_0. Do not reject H_0. (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.) (, )

Explanation / Answer

(a) Drivers total Calories x_bar = 2827   Drivers total Calories s = 116.962 Drivers Alcohol x_bar = 0.25 Drivers Alcohol s = 1.169 Conductors total calories x_bar = 2845 Conductors total calories s = 128.996 Conductors Alcohol x_bar = 0.35 Conductors Alcohol s = 1.048

(b) here the test statistic = (x1_bar - x2_bar) / sqrt(s1^2 / n1 + s2^2 / n2) We have been given in (a) x1_bar = 2827, x2_bar = 2845, s1 = 116.962 , s2 = 128.996, n1 = 95, n2 = 65. Using this, we get t = -0.899. We are conducting lower tailed test, where H_o : mu1 = mu2 and H_1 : mu_1 < mu_2. Now for conservative two sample t-test, degrees of freedom is = df = n2 - 1 = 64, since n2 < n1. Also alpha = 0.05. Using this the critical value = -1.669. Since t > critical value, we can't reject the null hypothesis and this means that there is not sufficient eveidence to conclude that conductors consume more calories than the drivers at alpha = 0.05

(c) Here, we are going to conduct a two tailed test. First group is drivers and second group is conductors. n1 = 95, n2 = 65, x1_bar = 0.25, x2_bar = 0.35, s1 = 1.169, s2 = 1.048. Again the test statistic t = (x1_bar - x2_bar) / sqrt(s1^2 / n1 + s2^2 / n2) = -0.565. Now for conservative two sample t-test, degrees of freedom is = df = n2 - 1 = 64, since n2 < n1. Also alpha = 0.05. Using this the lower critical value = -1.998. Since t is greater than the lower critical value, we can't reject the null hypothesis. So there is no significant observed difference in mean alcohol consumption.

(d) 95% confidence interval for mean daily alcohol consumption for conductors = (0.095, 0.605)

(e) 99 % confidence interval for the difference in mean daily alcohol consumption for drivers and conductors = (-0.569, 0.369).

As we can see in part (e), zero is included in this interval, which is also another indicator that there is not sufficient evidence in the mean alcohol consumption for drivers and conductors. This validates our answer in part (c)

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

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