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 a significance level equal to 0.05,assuming that the null hypothesis of equal means has been rejected,the Tukey-Kramer critical range is:
A)1.96.
B)approximately 4.0.
C)Can't be determined without more information.
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 a significance level equal to 0.05,assuming that the null hypothesis of equal means has been rejected,the Tukey-Kramer critical range is:
A)1.96. 
B)approximately 4.0. 
C)Can't be determined without more information. 
D)None of the above.

Quizplus · Accepted Answer

Since the null hypothesis of equal means has been rejected, we know that there is a significant difference between the mean speeds of the three sign designs. Therefore, we can use the Tukey-Kramer critical range to determine which pairs of means are significantly different. The critical range is determined by the sample size (n) and the significance level (α). In this case, n = 30 and α = 0.05. Looking up the values in a Tukey-Kramer critical range table, we can see that the critical range is approximately 4.0. Therefore, any pair of means that differ by more than 4.0 is significantly different at the 0.05 level.

The State Transportation Department Is Thinking of Changing Its Speed