https://file.aiquickdraw.com/mathbot/file/1726443980385rxfyayiw.jpg

Let's go through the questions one by one:

1. **What is the value of the sample statistic?**
   - Crystal observed an average weight loss of **18.5 pounds** in her sample. This is the sample statistic.

2. **Which symbol is used for the statistic in this situation?**
   - The correct symbol is **\(\bar{x}\)**, which represents the sample mean.

3. **Which of the following is an accurate statement?**
   - The sample mean is 18.5, but the population mean is 20. Thus, the correct statement is:
     - **The average (mean) of the population of numbers is \(\mu = 20\).**

4. **Use the pictured simulated distribution of sample statistics to identify the percentage of simulated statistics that are like Crystal's observed statistic or less.**
   - According to the distribution, count the squares at or below 18.5. From the graph, this includes the squares to the left of the marked 18.5 line. You would then divide by the total number of simulations (100) to find the proportion.
     - **Count squares 18.5 and lower. Divide by 100.**

5. **Identify the proportion of simulated statistics that are like Crystal's observed statistic or less.**
   - From the simulation, we can see that the number of values less than or equal to 18.5 is 9 out of 100.
     - **9/100 = 0.09**.

Would you like more details or have any questions?

Here are five related questions for deeper understanding:
1. What is the difference between a sample mean and a population mean?
2. How does the sample size affect the accuracy of the sample mean in estimating the population mean?
3. What role does random sampling play in statistical analysis?
4. How does the shape of the distribution of simulated sample means provide information about sampling variability?
5. How would increasing the number of simulations impact the result?

**Tip**: In statistical studies, increasing the sample size generally results in more reliable estimates of population parameters, as it reduces the variability of the sample mean.

The population of all people who use a certain diet program lose an average (mean) of 20 pounds in a year from the diet. Crystal takes a random sample of 114 people who used the diet plan for a year, and she finds that they had an average weight loss of 18.5 pounds. A distribution of 100 simulated sample statistics is shown in a graph. Based on the distribution and the given information, answer the following questions:

1. What is the value of the sample statistic?
2. Which symbol is used for the statistic in this situation?
3. Which of the following is an accurate statement?
4. Use the pictured simulated distribution of sample statistics to identify the percentage of simulated statistics that are like Crystal's observed statistic or less.
5. Identify the proportion of simulated statistics that are like Crystal's observed statistic or less.

Learn how to analyze the sample mean and compare it with the population mean using a simulated distribution. This example discusses the case of a diet program with a population mean weight loss of 20 pounds and a sample mean of 18.5 pounds. Includes questions on statistical symbols, accurate statements, and proportions.

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