Math Problem Statement

A restaurant conducted a customer satisfaction survey. Initially, one-third of the people surveyed reported being satisfied. After making changes to the menu, a follow-up survey of 30 people revealed that 16 out of 30 were satisfied. The task is to analyze whether the satisfaction level improved, using hypothesis testing. Three experimental options are provided: 1. Toss a fair coin 30 times and record how many heads appear, repeating this 500 times. 2. Roll 30 fair dice and record how many times the number 10 appears, repeating this 500 times. 3. Roll 30 fair dice and record how many times the result is 2 or lower, repeating this 500 times.

Solution

The provided image contains a text excerpt written in Japanese. The text appears to describe a scenario where a restaurant conducted a survey regarding customer satisfaction. Initially, one-third of the respondents expressed satisfaction. After modifying the menu, another survey was conducted among 30 people, and 16 of them said they were satisfied.

The task involves analyzing whether customer satisfaction improved after the menu changes. The text mentions a hypothesis testing approach and provides three experimental options, asking which of them is most suitable for testing whether customer satisfaction has remained unchanged.

Here’s a summary of the experiments:

  1. (ア) Toss a fair coin 30 times and record how many heads show up, repeating this process 500 times.
  2. (イ) Roll 30 fair dice and record how many times the number 10 appears, repeating this process 500 times.
  3. (ウ) Roll 30 fair dice and record how many times the result is 2 or lower, repeating this process 500 times.

The problem asks to identify which of these experiments best fits the hypothesis that the satisfaction level has not changed (i.e., assuming that 16 out of 30 people being satisfied is just a random result).

Would you like me to analyze these experiments in more detail or explain the hypothesis testing approach for this scenario? Here are some related questions:

  1. What does it mean to conduct a hypothesis test in this context?
  2. How do probability and random sampling apply to customer satisfaction surveys?
  3. Why might rolling dice or flipping coins simulate the survey results?
  4. What is the null hypothesis in this scenario?
  5. How do we determine whether the survey results show a significant improvement?

Tip: When dealing with hypothesis testing, always define both the null hypothesis (no change or no effect) and the alternative hypothesis (there is a change or effect). This helps clarify the objective of the test.

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Math Problem Analysis

Mathematical Concepts

Probability
Statistics
Hypothesis Testing

Formulas

Binomial Distribution Formula: P(X = k) = (nCk) * p^k * (1-p)^(n-k)
P-value calculation in hypothesis testing

Theorems

Central Limit Theorem
Law of Large Numbers

Suitable Grade Level

Grades 11-12 or College-level Statistics