Question

1. a producer brings 130 individuals interested in “dramadies” to serve as an audience for a run through of the pilot episode for a new netflix series. there are two lead actors being considered for the starring role in the show, and each made a pilot for the show. at the end of the run through, the audience members rate the candidate they watched.

a) design a completely randomized experiment the tv producer can use.
b) design an experiment where the producer blocks by gender. then, describe what the benefit of blocking by gender would be.

Explanation:

Step1: Design a completely randomized experiment

• Assign each of the 130 audience members a unique number from 1 to 130.
• Use a random number generator to select 65 numbers. The audience members corresponding to these numbers will watch the pilot with lead - actor candidate A, and the remaining 65 will watch with lead - actor candidate B.
• After the run - through, collect the ratings from all 130 audience members.

Step2: Design a blocked experiment by gender

• First, divide the 130 audience members into two blocks: male and female (assuming we can determine the gender of each member).
• For the male block (let's say there are \(m\) males), assign half (or as close to half as possible) to watch the pilot with lead - actor candidate A and the other half to watch with candidate B. Do the same for the female block (let's say there are \(f\) females, \(m + f=130\)).
• After the run - through, collect the ratings.

Step3: Explain the benefit of blocking by gender

• Blocking by gender helps to control for the potential confounding variable of gender. If, for example, males and females have different preferences in lead - actors (which could be due to various factors like different cultural perceptions of masculinity/femininity in acting, or different life experiences that influence their view of on - screen characters), by blocking, we can more accurately assess the effect of the lead - actor candidate (the treatment) on the ratings. Without blocking, any difference in ratings could be due to either the lead - actor candidate or gender (confounding). By blocking, we reduce the variability within each block (male and female) that is due to gender, making it easier to detect the true effect of the lead - actor candidate on the ratings.

Answer:

a) Assign each of the 130 audience members a unique number from 1 to 130. Use a random number generator to select 65 numbers. The audience members corresponding to these numbers will watch the pilot with lead - actor candidate A, and the remaining 65 will watch with lead - actor candidate B. After the run - through, collect the ratings from all 130 audience members.
b) Divide the 130 audience members into two blocks: male and female. For the male block (with \(m\) males), assign half (or as close to half as possible) to watch the pilot with lead - actor candidate A and the other half to watch with candidate B. Do the same for the female block (with \(f\) females, \(m + f = 130\)). After the run - through, collect the ratings. The benefit of blocking by gender is that it helps to control for the potential confounding variable of gender. By blocking, we reduce the variability within each block (male and female) that is due to gender, making it easier to detect the true effect of the lead - actor candidate on the ratings.