6.0 Unit 6 Overview: Inference for Categorical Data: Proportions
josh argo
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What is Inference?
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.
Confidence Intervals
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%).
Significance Tests
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.
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✍️ Free Response Questions (FRQs)
👆 Unit 1: Exploring One-Variable Data
✌️ Unit 2: Exploring Two-Variable Data
🔎 Unit 3: Collecting Data
🎲 Unit 4: Probability, Random Variables, and Probability Distributions
📊 Unit 5: Sampling Distributions
⚖️ Unit 6: Inference for Categorical Data: Proportions
😼 Unit 7: Inference for Qualitative Data: Means
✳️ Unit 8: Inference for Categorical Data: Chi-Square
📈 Unit 9: Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
✏️ Blogs
Best Quizlet Decks for AP Statistics
- Unit 1 Key Terms (15-23%): Exploring One-Variable Data
- Unit 2 Key Terms (5-7%): Exploring Two-Variable Data
- Unit 3 Key Terms (12-15%): Collecting Data
- Unit 4 Key Terms (10-20%): Probability, Random Variables, and Probability Distributions
- Unit 5 Key Terms (7-12%): Sampling Distributions
- Unit 6 Key Terms (12-15%): Inference for Categorical Data: Proportions
- Unit 7 Key Terms (10-18%): Inference for Quantitative Data: Means
- Unit 8 Key Terms (2-5%): Inference for Categorical Data: Chi-Squared
- Unit 9 Key Terms (2-5%): Inference for Quantitative Data: Slopes
- Closing Thoughts
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