Image Courtesy of pixabay.com
Have you ever seen a statistic perhaps on Facebook or Twitter and had your doubts? Maybe you read a statistic such as this one: "The proportion of goofy footed snowboarders who contract cancer is higher than those that are regular footed."
Sounds pretty goofy right? The process that scientists and data analysis use to make that conclusion comes from a process called statistical inference. Inference is a process where a study is performed on a small sample of a population in which we compare two groups or perhaps one group to a given proportion. Through calculations involving the normal distribution, we can estimate what the true population parameter is or we can test a claim given in an article or study using our sample. To estimate a population parameter, we use a confidence interval and to test a claim, we use a significance test.
For this unit, we are going to be estimating population parameters involving categorical data. This means that our sample statistic will be a sample proportion and we will be using that to estimate, or test against, a population proportion. The first process we are going to use is a confidence interval. A confidence interval is an interval of numbers based on our sample proportion that gives us a range where we can expect to find the true population proportion. A confidence interval will be based on three things: sample proportion, sample size and confidence level (usually 95%).
When we are given a population parameter and we have some reason to believe that it is false, we can perform a significance test to check if that value is correct. With a significance test, we are going to estimate the probability of obtaining our collected sample from the sampling distribution of our size when we assume that the given population proportion is correct. If the probability of obtaining our collected sample is low given those two factors (claimed population proportion and our sample size), we might have reason to reject the claim or at least investigate it further.
✍️ Free Response Questions (FRQs)
👆 Unit 1: Exploring One-Variable Data
1.4Representing a Categorical Variable with Graphs
1.5Representing a Quantitative Variable with Graphs
1.6Describing the Distribution of a Quantitative Variable
1.7Summary Statistics for a Quantitative Variable
1.8Graphical Representations of Summary Statistics
1.9Comparing Distributions of a Quantitative Variable
✌️ Unit 2: Exploring Two-Variable Data
2.0 Unit 2 Overview: Exploring Two-Variable Data
2.1Introducing Statistics: Are Variables Related?
2.2Representing Two Categorical Variables
2.3Statistics for Two Categorical Variables
2.4Representing the Relationship Between Two Quantitative Variables
2.8Least Squares Regression
🔎 Unit 3: Collecting Data
3.5Introduction to Experimental Design
🎲 Unit 4: Probability, Random Variables, and Probability Distributions
4.1Introducing Statistics: Random and Non-Random Patterns?
4.7Introduction to Random Variables and Probability Distributions
4.8Mean and Standard Deviation of Random Variables
4.9Combining Random Variables
4.11Parameters for a Binomial Distribution
📊 Unit 5: Sampling Distributions
5.0Unit 5 Overview: Sampling Distributions
5.1Introducing Statistics: Why Is My Sample Not Like Yours?
5.4Biased and Unbiased Point Estimates
5.6Sampling Distributions for Differences in Sample Proportions
⚖️ Unit 6: Inference for Categorical Data: Proportions
6.0Unit 6 Overview: Inference for Categorical Data: Proportions
6.1Introducing Statistics: Why Be Normal?
6.2Constructing a Confidence Interval for a Population Proportion
6.3Justifying a Claim Based on a Confidence Interval for a Population Proportion
6.4Setting Up a Test for a Population Proportion
6.6Concluding a Test for a Population Proportion
6.7Potential Errors When Performing Tests
6.8Confidence Intervals for the Difference of Two Proportions
6.9Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
6.10Setting Up a Test for the Difference of Two Population Proportions
😼 Unit 7: Inference for Qualitative Data: Means
7.1Introducing Statistics: Should I Worry About Error?
7.2Constructing a Confidence Interval for a Population Mean
7.3Justifying a Claim About a Population Mean Based on a Confidence Interval
7.4Setting Up a Test for a Population Mean
7.5Carrying Out a Test for a Population Mean
7.6Confidence Intervals for the Difference of Two Means
7.7Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
7.8Setting Up a Test for the Difference of Two Population Means
7.9Carrying Out a Test for the Difference of Two Population Means
✳️ Unit 8: Inference for Categorical Data: Chi-Square
📈 Unit 9: Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
Best Quizlet Decks for AP Statistics
*ap® and advanced placement® are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.
© fiveable 2021 | all rights reserved.
2550 north lake drive
milwaukee, wi 53211