✍️ 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
⏱️ 3 min read
June 5, 2020
Sometimes in statistical studies, it is important to compare two different populations to see if they are different. For instance, what if we want to compare the weights of two types of apples: 🍏 vs. 🍎. Perhaps we believe that the weight of 🍎 is more than 🍏 or maybe we just think they are different. Either way, we have the statistical means to be able to check if the weights are different or if one weighs more than the other. One option of comparing these two populations is to create a confidence interval for the difference of two population means.
As with any act of statistical inference, we must check our conditions for inference prior to performing any calculations.
As always, it absolutely essential that your samples come from a randomized process since we seek to infer things about a population. Since we are dealing with two populations, both samples must be random. If you are performing an experiment to check the difference in two populations, you must verify that both samples were randomly assigned to treatments, not just randomly selected.
Since we are generally sampling without replacement, we must check to be sure that the samples are independent. We can use this by checking the 10% condition for both samples.
**NOTE: If doing an experiment, it is not necessary to check the 10% condition. A randomized experiment is sufficient for independence.
To check normality of a sampling distribution for the difference in two population means, we have to be sure that both samples have approximately normal sampling distributions. This can be done using the Central Limit Theorem (n≥30), verifying that both populations are normally distributed, or a boxplot of both samples show no strong skewness or apparent outliers.
To calculate a confidence interval for the difference in two population means, we must first calculate our point estimate and margin of error.
Our point estimate is what we believe the difference between the two populations is based off of our sample means. To find this, we simply subtract our two sample means.
Our margin of error is what we add/subtract to our point estimate to create our confidence interval. For a confidence interval for the difference of two population means, the formula for margin of error is below:
A much easier, more efficient way of calculating a confidence interval for the difference in two population means is to use technology such as a graphing calculator. On a TI-84, you would start by going into the stats menu, scrolling to test and selecting 2 Sample T Interval, where you would put in the given statistics to calculate the confidence interval.
Let's say that we have a bag of green apples and a bag of red apples and we want to estimate the difference in population means of the two types of apples. Our sample of 30 🍏s weigh a mean of 5 oz with a standard deviation of 0.2 oz and our sample of 30 🍎s weigh a mean of 4.5 oz with a standard deviation of 0.15 oz. Create and interpret a confidence interval for the difference in the two population means of the weights of green apples and red apples.
The easiest way to construct your interval is to use technology such as a graphing calculator to do so:
We always select " not pooled" doing two sample intervals and tests. This is because we do not know if the populations have equal variances. After calculating we get the following interval: (0.408, 0.592).
🎥Watch: AP Stats - Inference: Confidence Intervals for Means
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