Proj-7 - Proj-7 PDF

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Proj-7...

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MT230

MINITAB PROJECT SHEET 7 The traffic division of a certain county council carries out an investigation to examine the effect of three new methods of traffic control A, B and C on reducing the number of stationary vehicles at a traffic junction. Each of the three methods of traffic control, together with the existing method D, are operated five times over a twenty day period of four weeks excluding weekends. The number of vehicles (in 1000’s) stationary at the junction for more than three minutes are recorded and given as follows.

Method Method Method Method

A B C D

1.7 1.4 1.5 2.0

1.7 1.5 1.7 1.8

1.8 1.3 1.5 1.7

1.4 1.5 1.8 1.9

1.7 1.4 1.4 2.0

Do the methods of traffic control have the same effect?

Suggested procedure: (1) The approach to the data provided is to compare the means of the four independent samples using the F -test for a One-Way Classification. It is essential that the four samples are read correctly. Enter the response variable (“the number of vehicles”) in one column. The corresponding factor levels (A, B, C, D) should be entered in another column. Then use STAT/ANOVA/ONE-WAY, and, to inspect the data visually, in GRAPHS select INDIVIDUAL VALUE PLOT. (2) If the F -test suggests that the population means are not the same then it is sensible to investigate where the differences are using Multiple Comparisons. We can obtain confidence intervals for all pairwise differences µA − µB , µA − µC , etc. (a) The LSD approach: Use STAT/ANOVA/ONE-WAY, click on COMPARISONS and FISHER’S. An individual error rate is the probability of falsely rejecting a given null hypotheses that µi − µj = 0 (significance level of each individual test). Equivalently, this is a probability that the corresponding confidence interval will not contain the true difference µi − µj in group means (the default value is 5%). (b) Tukey’s method: Use STAT/ANOVA/ONE-WAY, click on COMPARISONS and TUKEY’S. A family error rate is the probability of falsely rejecting at least one null hypotheses (overall significance level). Equivalently, this is the probability of obtaining at least one confidence interval that do not contain the true difference in group means (the default value is 5%)....