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# Lesson 6 Homework Practice Compare Populations Answers

If you are looking for some help with your lesson 6 homework practice compare populations answers, you have come to the right place. In this article, we will explain what it means to compare populations, how to use sample statistics to make comparisons, and how to write an inference based on your results. We will also provide some examples and tips to help you with your homework.

## What does it mean to compare populations?

A population is a group of individuals or objects that share one or more characteristics. For example, the population of students in your school, the population of dogs in your neighborhood, or the population of books in your library. Sometimes, we want to compare two populations to see how they are different or similar. For example, we may want to compare the heights of boys and girls in your class, the weights of cats and dogs in your neighborhood, or the number of pages of fiction and nonfiction books in your library.

To compare populations, we need to use sample statistics. Sample statistics are numerical values that describe a characteristic of a sample. A sample is a subset of individuals or objects from a population. For example, if we want to compare the heights of boys and girls in your class, we may measure the heights of 10 boys and 10 girls randomly selected from your class. These 20 students are a sample from the population of students in your class. The mean (average) and the standard deviation (a measure of variation) of their heights are sample statistics that describe their height distribution.

## How to use sample statistics to compare populations?

To use sample statistics to compare populations, we need to look at two aspects: the center and the variation. The center tells us where the middle of the distribution is, and the variation tells us how spread out the distribution is. The most common measures of center are the mean and the median. The most common measures of variation are the range and the standard deviation.

To compare the centers of two populations, we can compare their means or medians. If one population has a higher mean or median than another population, it means that its distribution is shifted to the right on a number line. If one population has a lower mean or median than another population, it means that its distribution is shifted to the left on a number line.

To compare the variations of two populations, we can compare their ranges or standard deviations. If one population has a larger range or standard deviation than another population, it means that its distribution is more spread out on a number line. If one population has a smaller range or standard deviation than another population, it means that its distribution is more clustered on a number line.

## How to write an inference based on your results?

An inference is a logical conclusion based on evidence and reasoning. To write an inference based on your results, you need to do three things:

• State what you are comparing and what sample statistics you are using.

• State what you observe from comparing the sample statistics.

• State what you can infer about the two populations based on your observation.

Here is an example of how to write an inference based on your results:

Example: The double dot plot shows the test scores of two classes on a math test.

Source: Texas Instruments

Inference: I am comparing the test scores of two classes on a math test using their means and standard deviations. I observe that Class A has a higher mean (85) than Class B (75), and Class A has a smaller standard deviation (5) than Class B (10). I can infer that Class A performed better and more consistently on the math test than Class B.

## Conclusion

In this article, we have learned how to compare populations using sample statistics and how to write an inference based on our results. We have also seen some examples and tips to help us with our lesson 6 homework practice compare populations answers. We hope that this article has been helpful and informative for you. If you want to learn more about statistics and probability, you can check out the online resources that we have suggested. Happy learning!

## What are some common mistakes and misconceptions when comparing populations?

When comparing populations using sample statistics, it is important to avoid some common mistakes and misconceptions that may lead to incorrect or misleading conclusions. Here are some of them:

• Confusing the population with the sample. The population is the entire group of interest, while the sample is a subset of the population. The sample statistics are estimates of the population parameters, not the exact values. For example, if we want to compare the heights of boys and girls in your school, we cannot measure the heights of all the students in your school. We can only measure the heights of a sample of students and use them to estimate the mean and standard deviation of the population.

• Ignoring the sample size and variability. The sample size and variability affect how reliable and precise the sample statistics are. A larger sample size and a smaller variability usually result in a more accurate and consistent estimate of the population parameter. For example, if we want to compare the test scores of two classes on a math test, we cannot simply compare their means and standard deviations. We also need to consider how many students are in each class and how much variation there is in their test scores.

• Making causal claims based on observational data. Observational data are data that are collected without any intervention or manipulation by the researcher. They can only show associations or correlations between variables, not causation. For example, if we want to compare the gas mileage of cars and SUVs, we cannot conclude that driving a car causes a higher gas mileage than driving an SUV. There may be other factors that affect the gas mileage, such as the driving habits, road conditions, weather, etc.

If you want to check your understanding and improve your skills on comparing populations using sample statistics, you can do some practice problems and get feedback on your answers. Here are some ways to do that:

• You can use your textbook or workbook that accompanies your course. They usually have exercises and problems on comparing populations using sample statistics, along with answer keys and explanations.

• You can use online worksheets that are generated by websites such as K12 Workbook . They allow you to create and print worksheets on various topics, including comparing populations. You can customize your worksheets by choosing the number of questions, difficulty level, format, and answer key.

• You can use online quizzes that are provided by websites such as Khan Academy. They offer interactive quizzes on various topics, including statistics and probability. You can practice making inferences from random samples and get instant feedback on your answers.

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