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 typically represents the sample size in statistics. In this context, 'n' refers to the number of players in each random sample.
2. Identify the given information: The problem states that 100 random samples were taken, and each sample consisted of 40 players. This means the sample size (n) is the number of players in each sample.
3. Recall the definition of 'n': In a sampling distribution, 'n' represents the size of each individual sample, not the total number of samples. Here, the total number of samples is 100, but the size of each sample is 40.
4. Verify the context: The mean of the sampling distribution is provided as 26.7 hours, but this value is not directly relevant to determining 'n'. Focus on the sample size information provided in the problem.
5. Conclude the value of 'n': Based on the problem, the value of 'n' is the number of players in each sample, which is explicitly stated as 40.