Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}
\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \
1 & 43 & 37 & 41 & 43 \
2 & 46 & 38 & 45 & 45 \
3 & 43 & 39 & 42 & 46
\end{array}$
-Referring to Instruction 11-6,based on the Tukey-Kramer procedure with an overall level of significance of 0.05,the retailer would decide that the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.

Question

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
 $\begin{array}{lcccc}
\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \
1 & 43 & 37 & 41 & 43 \
2 & 46 & 38 & 45 & 45 \
3 & 43 & 39 & 42 & 46
\end{array}$
-Referring to Instruction 11-6,based on the Tukey-Kramer procedure with an overall level of significance of 0.05,the retailer would decide that the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.

Quizplus · Accepted Answer

The Tukey-Kramer procedure is a multiple comparison procedure that can be used to compare the means of several groups. In this case, the retailer is comparing the mean speeds of four brands of bicycles. The overall level of significance is 0.05, which means that the retailer is willing to accept a 5% chance of making a Type I error (i.e., concluding that there is a significant difference when there is actually no difference).The Tukey-Kramer procedure uses a studentized range distribution to calculate the critical values for the comparisons. The critical value for the comparison of two means is:$$q_{\alpha,k,v}=\frac{q_{\alpha,k,v}}{{\sqrt{2}}}$$where:* $$\alpha$$ is the overall level of significance* $$k$$ is the number of groups being compared* $$v$$ is the degrees of freedom for the error termIn this case, $$\alpha=0.05$$, $$k=4$$, and $$v=6$$. The critical value is:$$q_{0.05,4,6}=3.94$$The retailer can then use the critical value to compare the mean speeds of the four brands of bicycles. The mean speed for the Tornado brand is significantly different from the mean speeds for the other brands if the difference between the mean speeds is greater than the critical value.In this case, the difference between the mean speed for the Tornado brand and the mean speed for the Barth brand is 4.5 km/h. The difference between the mean speed for the Tornado brand and the mean speed for the Reiser brand is 3.5 km/h. The difference between the mean speed for the Tornado brand and the mean speed for the Shaw brand is 1.5 km/h.All of these differences are greater than the critical value of 3.94 km/h. Therefore, the retailer would conclude that the mean speed for the Tornado brand is significantly different from the mean speeds for the other brands.

Instruction 11-6 as Part of an Evaluation Program,a Sporting Goods

Instruction 11-6
as Part of an Evaluation Program,a Sporting Goods