For a new advertising campaign, a video game retailer is interested in including information on the average play time of their most popular game. They get 100 random samples of 40 players and obtain their play time to get a sampling distribution. The mean of the sampling distribution is 26.7 hours. In this example, what is the value of $n$?

• A. 100
• B. 40
• C. 27
• D. Unknown

Answer: (B)

Verified step by step guidance

1. Understand the problem: The question is asking for the value of 'n', which represents the sample size in the context of the sampling distribution. The problem states that 100 random samples of 40 players were taken, and the sampling distribution was created based on their play times.
2. Identify the relevant information: From the problem, we know that the retailer took 100 random samples, and each sample consisted of 40 players. The value of 'n' refers to the number of players in each sample.
3. Recall the definition of 'n': In statistics, 'n' typically represents the sample size, which is the number of observations or data points in a single sample.
4. Match the information to the definition: Since each of the 100 samples contains 40 players, the value of 'n' is the number of players in each sample, which is 40.
5. Conclude the solution: Based on the information provided, the value of 'n' is 40, as it represents the sample size for each of the 100 samples.