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Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about \(13 \%\) of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York).

Short Answer

Expert verified
Estimate the percentage as \(16.67\%\) from your group data. It's an approximate probability that a person selected at random wiggles their ears.

Step by step solution

01

Gather Data from the Group

Identify the total number of students or friends in your group. Next, ask each person if they can wiggle their ears and count how many can actually do it. For example, if you have 30 people in your group and 5 of them can wiggle their ears, you have your initial data set.
02

Calculate the Sample Percentage

To find the sample percentage of people who can wiggle their ears, divide the number of people who can wiggle their ears by the total number of people in the group, then multiply by 100 to convert it into a percentage. Using the previous example, if 5 out of 30 people can wiggle their ears, the percentage is \(\frac{5}{30} \times 100 = 16.67\%\).
03

Interpret the Result as an Estimate of Probability

Treat the calculated percentage as an estimate for the probability that a randomly chosen person from your group can wiggle their ears. This means that if the percentage is 16.67%, then there is approximately a 16.67% chance that a person selected at random from this specific group can wiggle their ears.
04

Comparison with National Statistics

Compare your calculated percentage with the national statistic of 13%. If your percentage is higher (like 16.67%), it indicates that your group might have a slightly higher prevalence of people who can wiggle their ears than the national average.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sample Percentage
Calculating a sample percentage is a cornerstone of statistical analysis. This process helps us understand the proportion of a sample group exhibiting a specific characteristic. In the context of ear wiggling, you begin by finding the total number of individuals in your group who can actually wiggle their ears. For instance, if you find that 5 out of 30 people can wiggle their ears, you have gathered the initial numbers needed.
To calculate the sample percentage, you take the number of ear wigglers, divide it by the total group, and then multiply by 100 to get a percentage. For example, the calculation would be \[ \frac{5}{30} \times 100 = 16.67\% \].
This percentage gives us an estimate of how commonly ear wiggling occurs within your sample group. This simple process turns observational data into meaningful statistics that can provide deeper insights.
Data Collection
Data collection is the foundation of any statistical study. It involves gathering information in a structured way to gain insights into specific questions or phenomena. For your ear-wiggling exercise, the starting point is to identify everyone in your group. This creates the pool from which you will gather data.
Ask each person in your group whether they can wiggle their ears. Record how many say "yes". This direct yes/no inquiry keeps the process simple and ensures accurate data collection.
A few tips for successful data collection include:
  • Ensuring the group size is manageable but diverse. Larger groups provide more reliable data.
  • Asking clear, simple questions.
  • Avoiding leading questions that might influence responses.
The quality and accuracy of your data are crucial for the reliability of your statistical findings.
Statistical Comparison
Statistical comparison allows us to take our local data and understand it in a larger context. It's done by comparing your sample percentage to other statistics, such as national averages.
If your sample shows that 16.67% of people can wiggle their ears, you can compare this to the national statistic of 13% provided in the exercise. A higher percentage in your group suggests that your sample has more ear wigglers than the national norm.
To make these comparisons:
  • Ensure your sample is representative of the wider population.
  • Understand that differences may arise due to sample size and variability.
  • Use comparisons as a starting point for further investigation, rather than definitive conclusions.
This step helps in validating your data and providing context to your findings, thereby opening the door for deeper inquiry into why your results might differ.

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Most popular questions from this chapter

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