ch 27 a traffic engineer wanted to study the delays in traffic movement at three traffic signal locations as…

ch 27 a traffic engineer wanted to study the delays in traffic movement at three traffic signal locations as measured by the number of seconds before the first car clears the intersection. the engineer selected three locations randomly from all the signals with similar amount of traffic, number of lanes, and turn and signal patterns. the engineer collected the following data on eight randomly chosen days: \nlocation mean std. dev. n \nsite 1 39.30 17.05 8 \nsite 2 11.38 10.14 8 \nsite 3 27.45 5.44 8 \nthe engineer obtains a statistics book and, after investigating, decides that analysis of variance is the appropriate method for his problem. after using technology the engineers obtains a p - value = 0.001. this tells the engineer that \n○ mean delays are the same because it is rare to have different delay times. \n○ mean delays at all three sites are different. \n○ the mean delay at site 2 is the smallest and mean delay at sites 1 and 3 are the same. \n● mean delays are different for at least two sites.

ch 27 a traffic engineer wanted to study the delays in traffic movement at three traffic signal locations as measured by the number of seconds before the first car clears the intersection. the engineer selected three locations randomly from all the signals with similar amount of traffic, number of lanes, and turn and signal patterns. the engineer collected the following data on eight randomly chosen days: \nlocation mean std. dev. n \nsite 1 39.30 17.05 8 \nsite 2 11.38 10.14 8 \nsite 3 27.45 5.44 8 \nthe engineer obtains a statistics book and, after investigating, decides that analysis of variance is the appropriate method for his problem. after using technology the engineers obtains a p - value = 0.001. this tells the engineer that \n○ mean delays are the same because it is rare to have different delay times. \n○ mean delays at all three sites are different. \n○ the mean delay at site 2 is the smallest and mean delay at sites 1 and 3 are the same. \n● mean delays are different for at least two sites.

Answer

Brief Explanations:

In ANOVA (Analysis of Variance), a small P - value (here, (P - value=0.001), which is less than common significance levels like 0.05) indicates that we reject the null hypothesis that all population means are equal. The alternative hypothesis for ANOVA is that at least two of the population means are different. It does not tell us that all three means are different (we would need post - hoc tests for that) or which specific means are different, just that there is a difference among at least two of the groups (sites, in this case). The first option is wrong because a small P - value suggests differences. The second option is wrong as ANOVA doesn't prove all three are different. The third option is wrong as ANOVA doesn't tell us about specific pairs being equal. So the correct interpretation is that mean delays are different for at least two sites.

Answer:

mean delays are different for at least two sites.