Stat 250.2 Fall 1999 Name ________________________________
Supplementary Homework  Sheet #12 Student ID __ __ __ - __ __ - __ __ __ __
 
A.  Complete the following ANOVA table:
 
Source
DF
SS
MS
F
P-Value
Factor (Between) 4 155.0           0.000
Error (Within)                         
Total 39 200.5                

 

B.  A traffic engineering study on traffic delay was conducted at intersections with signals on urban streets. Three types of signals were utilized: (1) pre-timed, (2) semi-actuated, and (3) fully actuated. Five intersections were used for each type of signal. The measure of traffic delay used in the study was the average stopped time per vehicle at each of the intersections (seconds/vehicle). The data follow:

 
Pretimed Semi-actuated Fully actuated
36.6 17.5 15.0
39.2 20.6 10.4
30.4 18.7 18.9
37.1 25.7 10.5
34.1 22.0 15.2

The following is the resulting ANOVA table and confidence intervals for each of the means:
 

Analysis of Variance
Source     DF        SS        MS        F        P
Factor      2    1202.6     601.3    52.35    0.000
Error      12     137.8      11.5
Total      14    1340.5
                                   Individual 95% CIs For Mean
                                   Based on Pooled StDev
Level       N      Mean     StDev  -------+---------+---------+---------
Pre         5    35.480     3.370                             (---*---) 
Semi        5    20.900     3.191           (---*---) 
Full        5    14.000     3.594  (----*---) 
                                   -------+---------+---------+---------
Pooled StDev =    3.389                16.0      24.0      32.0
  1. What type of study was conducted?  A comparative observational study or a randomized comparative experiment?
  2. What makes this problem an analysis of variance problem?
  3. What are the null and alternative hypotheses?
  4. Based on the P-value, do we reject or not reject the null hypothesis? Write a statement that summarizes the conclusion that can be made.
  5. Do the individual 95% confidence intervals for the means produce a similar conclusion?
  6. Can we definitively conclude that the type of traffic signal causes traffic delays?  Why or why not?

C.  Data were collected on student teachers relative to their use of certain teaching strategies that had been presented to them in preservice education. There were 28 student teachers who had learned to use the strategies (9 in 1979, 9 in 1980, and 10 in 1981). In 1978, there were 6 teachers who did not learn to use the strategies and they were used as a control group. The investigator recorded the average number of strategies used per week by each of the student teachers during their student teaching assignments. The investigator wanted to know whether the number of strategies used by the student teachers were different among the years. The resulting data were:

Average Number of Different Strategies Used
1978 1979 1980 1981
6.88 7.25 10.85 7.29
5.40 10.50 7.43 14.38
16.00 8.43 6.71 6.00
9.80 8.63 7.60 5.00
7.63 8.63 9.71 5.38
5.00 7.00 5.57 14.14
  11.13 8.71 9.25
  7.25 5.86 5.71
  10.38 7.20 7.35
      10.75
       
  1. Use Minitab to create a graph (like side-by-side boxplots or dotplots) that allows you to visually compare the groups.
  2. Use Minitab to determine the ANOVA table.
  3. Specify the appropriate null and alternative hypotheses.
  4. Is there sufficient evidence at the 0.05 significance level to conclude that the average number of different strategies used by the student teachers differed over the four years?