Now the hard work is done. You have written your hypotheses, checked your conditions, calculated your statistics, but now what? What does this mean? 🤷🤷
Our basic conclusion hinges on one of two outcomes: you are either going to reject your null or fail to reject your null. These are based off of the probability of obtaining our test statistic.
❇️Important Note: NEVER ACCEPT YOUR Ho or Ha! ALWAYS REJECT/FAIL TO REJECT!**
The first, and most common way to conclude our significance test is using our p-value that is generated by our calculator. Remember, our p-value is the probability of obtaining our sample if we have a normal sampling distribution with the null value as our center. We conclude by comparing our p-value to our significance level (which is usually 0.05 unless otherwise noted). If our p-value is lower than our significance level (or our 𝞪), this means that it is unlikely to occur by random chance. Therefore, we have reason to reject our Ho.
If our p-value is not lower than our significance level (or alpha level), then we fail to reject our Ho (not accept). This means that we do not have evidence to reject our Ho in favor of our Ha, but we also don't have evidence to completely accept our Ho as fact.
While a p-value is the most common way to conclude a test, we can also use our z-score to conclude a test. Remember that a z-score is how many standard deviations we are above/below the mean. Therefore, if we have a z-score higher than 2, it is pretty unlikely to occur by natural chance (since we have checked our normal condition and know that we are dealing with a normal sampling distribution). This comes from the Empirical Rule that states that 95% of our data in a normal distribution falls within 2 standard deviations. Therefore, a z-score higher than 2 (or lower than -2) signifies that the probability of it occurring is likely less than 0.05. So we can conclude the same way as we did above with a p-value. It is especially easy to make a reject Ho decision when our z-score is really large (like 4+ or -4-). If our z-score is in the range of -2 to 2, it is really hard to reject our Ho, so we will likely fail to reject without further information.
Here is the template you can follow when concluding a one proportion z test for population proportion (or a 1-Prop Z Test):
The big three things you need to have in your conclusion to maximize our credit are:
Compare p-value to significance level
Make a decision (reject or fail to reject)
Include context with inference to TRUE POPULATION PROPORTION.
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🎥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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