If you're looking back at the snowboarder study from the Unit 6 Overview, "being normal" here isn't referring to being regular footed as a snowboarder. 🤣🤣
In fact, the term "normal" has much larger statistical implications. When we are performing statistical inference, our calculations are very largely based on sampling distributions of a proportion, which yep, you guessed it, are normal curves.
If you refer back to Unit 1.1, we know that a lot of fancy Calculus calculations can allow us to calculate probabilities using these normal curves. When testing a statistical claim or estimating a population proportion, we need the normal curve to calculate the probability in our sampling distribution (see Unit 5). By taking our sample and standardizing it to a common density curve, we can use calculator functions or our z-score chart to make inference using the normal curve.
To check if our sampling distribution is normal, we need to verify that the expected successes and expected failures of our study is at least 10. This is known as the Large Counts Condition.
In formula form, this is np≥10 and n(1-p)≥10.
This verifies that our sampling distribution is normal and we can continue with z-scores to calculate our probabilities or intervals.
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Let's say that we believe that hockey players have a 95% chance of breaking a bone at some point in their life. We decide to test that claim by taking a sample of 500 retired hockey players and asking them if they have ever broken a bone. To verify that we can use the normal curve in this test/interval, we would list the following:
✔️500(0.95)≥10 & 500(0.05)≥10
✔️475≥10 & 25≥10
Since both calculations come out to be more than 10, we can use our proportion from our sample to check if the 95% value given is actually true.
🎥Watch: AP Stats - Normal Distributions
✍️ 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)
Is AP Statistics Hard? Is AP Statistics Worth Taking?
Best Quizlet Decks for AP Statistics
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