In Exercises 4 and 5, determine whether the number is a parameter...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

1. Intro to Stats and Collecting Data

Intro to Stats

Statistics

1. Intro to Stats and Collecting Data

Intro to Stats

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1:21 minutes

Problem 1.CR.4

Textbook Question

In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.

In 2021, the median annual salary of a first-year chemist was $58,700.

Verified step by step guidance

Understand the difference between a parameter and a statistic: A parameter is a numerical value that describes a characteristic of a population, while a statistic is a numerical value that describes a characteristic of a sample drawn from the population.

Identify the context of the given number: The problem states that the median annual salary of a first-year chemist in 2021 was $58,700.

Determine whether the number refers to the entire population or a sample: If the number represents all first-year chemists in 2021, it is a parameter. If it represents only a subset (sample) of first-year chemists, it is a statistic.

Analyze the phrasing of the problem: The problem does not explicitly mention that the number is based on a sample, so it is reasonable to assume it refers to the entire population of first-year chemists in 2021.

Conclude: Since the number likely represents the entire population, it is a parameter. If additional information were provided indicating it was based on a sample, it would instead be a statistic.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Parameter

A parameter is a numerical value that summarizes a characteristic of a population. It is a fixed value that is usually unknown and can only be estimated through sample data. In the context of statistics, parameters are often denoted by Greek letters, such as μ for the population mean or σ for the population standard deviation.

Statistic

A statistic is a numerical value that summarizes a characteristic of a sample drawn from a population. Unlike parameters, statistics can vary depending on the sample selected and are used to estimate population parameters. Common examples include sample means (x̄) and sample proportions (p̂), which help infer characteristics about the larger population.

Median

The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers. It is particularly useful for understanding the distribution of salaries, as it is less affected by extreme values than the mean.

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In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.In 2021, the median annual salary of a first-year chemist was $58,700.