When interpreting a confidence interval for the difference in two population proportions, we need to show that the bounds given by the confidence interval give us an estimate of what the difference in our two population proportion are within. Our interpretation and interval is also strongly based on what our confidence level is. The standard confidence level is 95%.
When completing a confidence interval on the AP Statistics Exam, you will generally be graded on if you included the following three components:
👉 Including confidence level (given in problem)
👉 Including that our interval is making inference about the difference in population proportions, not sample proportions.
👉 Including context of the problem.
If you do these three things and get the correct answer, you will be on your way to 💯.
When we are testing a claim using a confidence interval, we want to see if 0 is included in our interval. If 0 is included in our interval, it is quite possible that there is no difference in the two population proportions we are testing. If 0 is not included in our interval, we have reason to suspect that the two population proportions are in fact different.
Image Courtesy of cbssports
Recall from Unit 6.8 we constructed a confidence interval for the difference in proportions for shots made for Michael Jordan and Lebron James. We got the following output from our calculator:
A correct way to interpret this would be:
"We are 95% confident that the true difference in the population proportions for shots made between Michael Jordan and Lebron James is between (0.063, 0.133). Since 0 is not included in our interval, we have reasonable evidence that the two population proportions are actually different"
So it appears that MJ is better than Lebron. ¯\_(ツ)_/¯
However, some things to note here is that we took a sample from both of their first seasons. If we refer back to basketball-reference.com and compare the two players 10th seasons in the league, we might find a VERY different result. Another possible confounding variable is the teammates these two players have been surrounded by throughout their career.
🎥Watch: AP Stats - Inference: Confidence Intervals for Proportions
✍️ 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
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