Question

Lifetimes of Flashlight Batteries.Two different options are under consideration for comparing the lifetimes of four brands of flashlight battery, using 20 flashlights.

(a) One option is to randomly divide 20 flashlights into four groups of 5 flashlights each and then randomly assign each group to use a different brand of battery. Would this statistical design be a completely randomized design or a randomized block design? Explain your answer.

(b) Another option is to use 20 flashlights - five different brands of 4 flashlights-each and randomly assign the 4 flashlights of each sign be a completely randomized design or a randomized block design? Explain your answer.

Short answer

Part (a) Completely Randomized Design.

Part (b) Randomized Block Design.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Two different options are under consideration for comparing the lifetimes of four brands of flashlights battery, using 20 flashlights.

(a) One option is to randomly divide 20 flashlights into four groups of 5 flashlights each and then randomly assign each group to use a different brand of battery. Would this statistical design be a completely randomized design or a randomized block design? Explain your answer.

(b) Another option is to use 20 flashlights - five different brands of 4 flashlights-each and randomly assign the 4 flashlights of each sign be a completely randomized design or a randomized block design? Explain your answer.

Part (a) Step 2. Explanation for option one.

According to option one, the 20 flashlights were separated into four groups of five flashlights each, each group was randomly assigned to utilize a different type of battery.

The above-said experiment is done in a truly randomized design in which all experimental units were assigned randomly among all treatments.

Therefore, the given Completely Randomized Design is a statistical design.

Part (b) Step 1. Explanation for option one.

In the second option, it is given 20 flashlights were divided into five groups, each group with four flashlights.

Then the four flashlights in each group were assigned four different brands of battery at random, as is done in a randomized block design, where the experimental units are assigned randomly among all the treatments separately within each block.

Therefore, this statistical design is a Randomized Block Design.