TABLE 11-11
A student team in a business statistics course designed an experiment to investigate whether the brand of bubblegum used affected the size of bubbles they could blow.To reduce the person-to-person variability,the students decided to use a randomized block design using themselves as blocks.
Four brands of bubblegum were tested.A student chewed two pieces of a brand of gum and then blew a bubble,attempting to make it as big as possible.Another student measured the diameter of the bubble at its biggest point.The following table gives the diameters of the bubbles (in inches)for the 16 observations.
-True or False: Referring to Table 11-11,the relative efficiency means that 1.0144 times as many observations in each brand would be needed in a one-way ANOVA design as compared to the randomized block design in order to obtain the same precision for comparison of the different means.

Question

TABLE 11-11
A student team in a business statistics course designed an experiment to investigate whether the brand of bubblegum used affected the size of bubbles they could blow.To reduce the person-to-person variability,the students decided to use a randomized block design using themselves as blocks.
Four brands of bubblegum were tested.A student chewed two pieces of a brand of gum and then blew a bubble,attempting to make it as big as possible.Another student measured the diameter of the bubble at its biggest point.The following table gives the diameters of the bubbles (in inches)for the 16 observations. 
-True or False: Referring to Table 11-11,the relative efficiency means that 1.0144 times as many observations in each brand would be needed in a one-way ANOVA design as compared to the randomized block design in order to obtain the same precision for comparison of the different means.

Quizplus · Accepted Answer

The relative efficiency between a randomized block design and a one-way ANOVA design is typically calculated as the ratio of the sum of squares between blocks in the randomized block design to the sum of squares between treatments in the one-way ANOVA design. In this case, the relative efficiency is given by:

SS(blocks) / SS(treatments) = (0.1562 / 0.1539) = 1.0144

This means that, on average, 1.0144 times as many observations in each brand would be needed in a one-way ANOVA design as compared to the randomized block design in order to obtain the same precision for comparison of the different means. Therefore, the statement is true.

TABLE 11-11 a Student Team in a Business Statistics Course Designed an Designed