The text in the image presents a scenario involving a survey conducted at a restaurant and a follow-up survey after menu improvements. Here's a detailed breakdown of the problem and the three experimental options:

Summary of the Scenario:

• Initial Survey: In the initial survey, 1 out of 3 people responded that they were "satisfied" with the restaurant.

• Menu Improvement: The restaurant improved its menu and conducted the survey again.

• New Survey Results: In the second survey, 16 out of 30 people said they were "satisfied."

• Question: Based on these results, can we conclude that the satisfaction level of the restaurant has increased compared to before? The problem wants to use a hypothesis-testing approach to investigate this question.

  The task is to determine which of the three experiments listed below (denoted by (ア), (イ), (ウ)) is the most suitable for this hypothesis test and to provide a reason.

The Three Experiments:

1. (ア): Perform 500 trials of flipping a fair coin 30 times and record the number of heads.
2. (イ): Perform 500 trials of rolling 30 fair dice and record the number of times a "1" appears on the first roll.
3. (ウ): Perform 500 trials of rolling 30 fair dice and record the number of times a "2" or lower appears.

Analysis:

• The key to answering this question lies in comparing the probability distributions from the experiments with the results of the satisfaction survey. Since we're working with the idea that 16 out of 30 people are satisfied, the correct experimental setup would be one that mirrors the probability of getting "successes" in a situation with binary outcomes (e.g., satisfied vs. not satisfied).

• (ウ) is the best choice because it involves rolling dice and counting the number of times a specific event occurs (rolling a "2" or lower). This could represent the probability of "satisfaction" being somewhat rare but observable, similar to the 16 out of 30 results in the satisfaction survey.

Would you like more details on hypothesis testing or the reasoning behind choosing (ウ)? Here are some related questions to expand on this topic:

1. What is hypothesis testing, and how does it relate to this scenario?
2. How do you calculate the probability of a "success" in binomial experiments?
3. How does experiment (ウ) model a real-world scenario like customer satisfaction surveys?
4. What statistical tools are commonly used to compare two proportions (before and after improvements)?
5. Can this experiment be used to calculate a confidence interval for customer satisfaction?

Tip: In binomial probability, outcomes are often framed as either "success" or "failure," making it ideal for analyzing customer survey results with only two outcomes (satisfied or not satisfied).