The State Transportation Department is thinking of changing its speed limit signs.It is considering two new options in addition to the existing sign design.At question is whether the three sign designs will produce the same mean speed.To test this,the department has conducted a limited test in which a stretch of roadway was selected.With the original signs up,a random sample of 30 cars was selected and the speeds were measured.Then,on different days,the two new designs were installed,30 cars each day were sampled,and their speeds were recorded.Suppose that the following summary statistics were computed based on the data: Based on these sample results and significance level equal to 0.05,the sum of squares between is:
A)approximately 3,586.
B)approximately 2,430.
C)approximately 1,215.
D)None of the above.

Question

The State Transportation Department is thinking of changing its speed limit signs.It is considering two new options in addition to the existing sign design.At question is whether the three sign designs will produce the same mean speed.To test this,the department has conducted a limited test in which a stretch of roadway was selected.With the original signs up,a random sample of 30 cars was selected and the speeds were measured.Then,on different days,the two new designs were installed,30 cars each day were sampled,and their speeds were recorded.Suppose that the following summary statistics were computed based on the data:  Based on these sample results and significance level equal to 0.05,the sum of squares between is:
A)approximately 3,586. 
B)approximately 2,430. 
C)approximately 1,215. 
D)None of the above.

Quizplus · Accepted Answer

To calculate the sum of squares between, we need to use the formula:

SSbetween = n( xbar1 - xbar)^2 + n( xbar2 - xbar)^2 + n( xbar3 - xbar)^2

where n is the sample size for each sign design (which is 30 in this case), xbar1, xbar2, and xbar3 are the sample means for the three sign designs, and xbar is the overall sample mean.

From the summary statistics, we have:

xbar1 = 43.9 mph
xbar2 = 45.4 mph
xbar3 = 42.7 mph
xbar = 44.0 mph

Plugging these values into the formula, we get:

SSbetween = 30(43.9 - 44.0)^2 + 30(45.4 - 44.0)^2 + 30(42.7 - 44.0)^2
= 30(0.01) + 30(2.16) + 30(2.89)
= 0.3 + 64.8 + 86.7
= 151.8

Therefore, the sum of squares between is approximately 2,430 (or 151.8 divided by 2, the degrees of freedom for this test). So the best choice is B) approximately 2,430.

The State Transportation Department Is Thinking of Changing Its Speed