✍️ 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
Now that we have checked out conditions for inference, we can calculate the two aspects that are necessary for a significance test: our test statistics and p-value.
The first and necessary aspect of our calculations is calculating our t-score. Since we are dealing with quantitative data (means), we need to find our degrees of freedom first.
When calculating by hand, we will take the smaller of the two samples and subtract 1. This is the same as we did in Unit 7.5 with 1 sample.
When performing the test with technology such as a graphing calculator, the degrees of freedom will be given with the output.
To calculate our critical value, we used the typical formula:
To make it more specific for a t-score with the difference of two population means, our formula simplifies to:
This can be found on the Formula Sheet by simplifying the given formulas.
Now that we know our appropriate degrees of freedom and our t-score, we can refer to our Formula Sheet and refer to the appropriate row for our df. Looking across the tow, find the t-score value that is closest to the one you calculated for the t-score. Use the tail probability that most closely coordinates to your t-score.
A more exact way of calculating the p-value is to perform a 2 sample t-test in some form of technology such as a graphing calculator. As with any t-procedure, you are given the option of typing in the statistical information or entering in the data in list 1.
Once you enter the test in, the output gives you the t-score, df and p-value for your test. On the AP test, it is essential that you write down ALL 3 of these on your response to receive full credit.
For our green bean example from Unit 7.8, this is what our input would look like:
And our output would be as follows:
Now that you have the numbers you need, you can check the statistical claim of the null hypothesis.
As with any significance test, we are checking to see if our p is lower than the significance level. If our p is low, we reject the null with convincing evidence of the alternate hypothesis. If the p is not lower than the significance level, we fail to reject the null hypothesis.
Once you make your decision, you should be able to see if in fact there is a difference in your two populations.
For our green bean example, our conclusion would be as follows:
Since our p value is essentially 0 and less than 0.05, we reject our Ho. We have convincing evidence that the true mean number of green beans picked from Field A differs from that picked in Field B.
I made sure to compare our p-value to our significance level, reject/fail to reject Ho, and have evidence/not have evidence of the Ha. Also, my answer is in context.
🎥Watch: AP Stats - Review of Inference: z and t Procedures
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