✍️ 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
⏱️ 3 min read
June 5, 2020
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When given a multiple choice question regarding inferential procedures, it is almost always going to pertain to selecting the correct procedure, interpreting a p-value or drawing a conclusion given a p-value.
When asked to select a correct procedure, the best way of approaching the problem is to ask yourself 2 questions:
Am I dealing with means or proportions?
Do I have 1 or 2 samples?
This will help you to determine if you are running a 1/2 sample/prop t/z test/interval.
Those 2 questions are the guiding factor in answering what type of test/interval we will run.
Some special cases to note: when given one sample in an experimental study where every unit receives both treatments, this is a matched pairs t-test, not a 2 sample t test. Also, when dealing with multiple proportions (more than 2), a chi-square test may be necessary.
When asked to interpret a p-value, remember that it is the probability of obtaining your given sample from the sampling distribution of that particular sample size, given that the true mean/proportion is what the null hypothesis claims.
In a hypothesis test where the Ho: p=0.2 and the Ha: p<0.2, we collect a sample of 100 where our p-hat is 0.15. Our significance test reveals a p-value of 0.11. Interpret this p-value.
A p value of 0.11 tells us that the probability of obtaining a sample of 100 where the success rate was 0.15 or lower would happen approximately 11% of the time, given our normal sampling distribution when n=100.
In drawing a conclusion from an inference procedure, we are generally comparing a p-value to a significance level. You can follow the chart below in making your decision:
|p<alpha: Reject the Ho||We have significant evidence of the Ha (in context).|
|p>alpha: Fail to Reject the Ho||We do not have significant evidence of the Ha (in context).|
We never accept a Ho or Ha!
When dealing with free response questions requiring inferential procedures, we usually see one of the following 2 prompts:
Do the data give convincing evidence... (Significance Test)
Construct and interpret a ___% confidence interval (Confidence Interval)
Both of these stems can follow the SPDC Template outlined below:
When performing a confidence interval, here is where you should state what the parameter(s) are for our population(s) that we are estimating.
When performing a significance test, this is the place in the problem when you should write the hypotheses for your questions. Also, label and identify your parameters.
Remember, your Ho will always have an equal sign and your Ha will always have some form of inequality (<, > or not equal to)
This is where we check our three conditions for inference: Random, Independent and Normal. This is basically the same from confidence interval or significance test, but varies based on the type of data (categorical or quantitative).
Start out by identifying the test/interval you are performing. This is usually which function you are selecting in the STATS menu of your calculator. Write this down!
Then write out your answer from your calculator:
Confidence Intervals: Just the interval is sufficient
Significance Test: Critical Value, p-value, and df (if necessary)
This is where you follow templates given throughout the unit.
For confidence intervals: "I am ___% confident that the true _____ of __________ is between (__, __).
For significance tests: "Since the p(</>) alpha, I (fail to reject/reject) the Ho. There (is/is not) convincing evidence of Ha (in context of problem)."
🎥Watch: AP Stats - Review of Inference: z and t Procedures
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