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A p-value for a significance test is the proportion of possible samples of a given size that are equal to or less than/greater than our given sample. This probability is computed with the belief that the hypothesized value in the null hypothesis is true. In essence, the p-value is the probability of obtaining that given sample.
If our p-value is low, this means that it is highly unlikely that our sample would be chosen randomly. This could be due to one of three things:
Legitimate random chance (I mean, someone wins the lottery every now and then right? 🤑🤑)
Some form of sampling bias (This is why we check that our sample is random before proceeding to a significance test)
Our hypothesized value in the null hypothesis is actually false. This is what we are checking with our significance test.
To be sure that this didn't occur by random chance, we should maybe check 2 or 3 random samples. If we get the same result each time, the consistency leads us to believe we are up to something (no one wins the lottery three times in a row). To be sure it isn't sampling bias, we make sure we have random samples. If both of those are met, there must be a problem with null hypothesis value.
In the recent issue of Sports Unlimited, Jackie reads that a right-handed hockey player scores on approximately 5% of their shots. To test this claim, Jackie watches 15 random hockey games and records 921 shots from random, right-handed hockey players. She finds that they scored on 60 of those shots. After calculating her z-score and p-value, she finds that her p-value is essentially 0.017. Interpret this p value.
This p-value means that of all possible samples of 921 shots from right handed players, approximately 1.7% of those samples would have at least 60 shots. This sample was random from the given information, so no obvious sampling bias. It could be that Jackie just hit the jackpot and watched the right players to have such a high goal scoring percentage. She could check this by redoing the experiment a few times. The other option is that the 5% isn't actually correct. Maybe that hypothesized percentage is a bit higher...🤔
🎥Watch: AP Stats - Inference: Hypothesis Tests 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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