Question

A researcher wants to find out which of four routes is the fastest way to drive from a suburb to downtown Chicago. He divides 20 participants into four groups, and he times each of them as they go on their assigned route. The following are the number of minutes for each route:

                Route 1 Route 2 Route 3 Route 4

                __________________________________

                  22 25 26 26

                  26 27 29 28

                  25 28 33 27

                  25 26 30 30

                  31 29 33 30

                __________________________________

        

a. What is the appropriate statistic here?

b. Run the appropriate statistic in SPSS and report the results.

c. Spell out what the results tell the researcher about the options for the daily commute from the suburb to downtown: which, if any, route should be preferred?

Answer 1

Result:

A researcher wants to find out which of four routes is the fastest way to drive from a suburb to downtown Chicago. He divides 20 participants into four groups, and he times each of them as they go on their assigned route. The following are the number of minutes for each route:

                Route 1 Route 2 Route 3 Route 4

                __________________________________

                  22 25 26 26

                  26 27 29 28

                  25 28 33 27

                  25 26 30 30

                  31 29 33 30

                __________________________________

        

a. What is the appropriate statistic here?

Since there are 4 routes( groups) and we want to compare the means of the four groups, ANOVA is appropriate here.

b. Run the appropriate statistic in SPSS and report the results.

Ho: µ1= µ2= µ3= µ4

H1: At least one of the mean is different from the others

SPSS output:

Descriptives
time
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
Route 1	5	25.80	3.271	1.463	21.74	29.86	22	31
Route 2	5	27.00	1.581	0.707	25.04	28.96	25	29
Route 3	5	30.20	2.950	1.319	26.54	33.86	26	33
Route 4	5	28.20	1.789	0.800	25.98	30.42	26	30
Total	20	27.80	2.840	0.635	26.47	29.13	22	33

ANOVA
time
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	52.800	3	17.600	2.805	0.073
Within Groups	100.400	16	6.275
Total	153.200	19

Calculated F=2.805, P=0.073 which is > 0.05 the level of significance. Ho is not rejected.

c. Spell out what the results tell the researcher about the options for the daily commute from the suburb to downtown: which, if any, route should be preferred?

We conclude that there is no significant difference in average number of minutes commute between the four routes. The test does not suggest any preference. However the average time for the route 1 is smaller than others.