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Unit 6: Inference for Categorical Data: Proportions

11 dot points across 11 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you compute the test statistic and P-value and conclude a test comparing two proportions?

Topic 6.11 Carrying Out a Test for the Difference of Two Population Proportions: compute the two-sample z test statistic using the pooled standard error, find the P-value, and state a conclusion in context.
A focused answer to AP Statistics Topic 6.11, on computing the two-sample z statistic with the pooled standard error, finding the P-value, and stating a conclusion in context, with a full worked two-proportion test.
11 min answer →

How do you compute the test statistic and P-value and state a conclusion for a one-sample proportion test?

Topic 6.6 Concluding a Test for a Population Proportion: compute the standardized z test statistic and P-value for a one-sample proportion test, compare to the significance level, and state a conclusion in context.
A focused answer to AP Statistics Topic 6.6, on computing the standardized z statistic and P-value for a one-sample proportion test using the null value, comparing to alpha, and stating a conclusion in context, with a full worked test.
11 min answer →

How do you construct a confidence interval for the difference between two population proportions?

Topic 6.8 Confidence Intervals for the Difference of Two Proportions: check the conditions and construct a two-sample z-interval for the difference between two population proportions, using the unpooled standard error.
A focused answer to AP Statistics Topic 6.8, on building a two-sample z-interval for the difference of two population proportions - checking conditions for both samples and using the unpooled standard error - with a full worked interval.
11 min answer →

How do you construct and interpret a confidence interval for a population proportion?

Topic 6.2 Constructing a Confidence Interval for a Population Proportion: identify the conditions, compute the point estimate, critical value, standard error, and margin of error, and construct and interpret a one-sample z-interval for a proportion.
A focused answer to AP Statistics Topic 6.2, on building a one-sample z-interval for a population proportion - checking conditions, finding the critical value, standard error, and margin of error - with a full worked interval and contextual interpretation.
11 min answer →

What does a P-value measure, and how is it interpreted in the context of a test?

Topic 6.5 Interpreting P-Values: define the P-value as the probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one observed, and interpret it in context.
A focused answer to AP Statistics Topic 6.5, on defining the P-value as the probability under the null of a result at least as extreme as observed, interpreting small and large P-values, and avoiding common misreadings, with a worked interpretation.
9 min answer →

Why does the approximately normal sampling distribution of a sample proportion make inference about a population proportion possible?

Topic 6.1 Introducing Statistics: Why Be Normal?: explain how the approximately normal sampling distribution of a sample proportion lets us quantify uncertainty and make inferences about an unknown population proportion.
A focused answer to AP Statistics Topic 6.1, on why the approximately normal sampling distribution of a sample proportion is the engine that lets us build confidence intervals and significance tests about an unknown population proportion.
9 min answer →

How do you use a confidence interval for a difference of two proportions to justify a claim?

Topic 6.9 Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions: use a two-sample proportion interval to judge whether a difference exists and to evaluate claims about the size and direction of that difference.
A focused answer to AP Statistics Topic 6.9, on using a two-sample proportion confidence interval to judge whether two proportions differ and to assess claims about the size and direction of the difference, with worked justifications.
9 min answer →

How do you use a confidence interval for a proportion to justify a claim about the population?

Topic 6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion: use a confidence interval for a proportion to evaluate whether a claimed value is plausible, and discuss the effect of confidence level and sample size on the interval.
A focused answer to AP Statistics Topic 6.3, on using a one-sample proportion confidence interval to judge whether a claimed value of p is plausible, and explaining how confidence level and sample size change the interval, with worked justifications.
9 min answer →

What are Type I and Type II errors, and how do significance level, sample size, and effect size affect them?

Topic 6.7 Potential Errors When Performing Tests: distinguish Type I and Type II errors and their consequences, define the power of a test, and explain how significance level, sample size, and effect size affect error probabilities and power.
A focused answer to AP Statistics Topic 6.7, on Type I and Type II errors, their real-world consequences, the power of a test, and how alpha, sample size, and effect size change error rates and power, with worked reasoning in context.
10 min answer →

How do you state the hypotheses and check the conditions for a significance test about a population proportion?

Topic 6.4 Setting Up a Test for a Population Proportion: state null and alternative hypotheses about a population proportion, identify the significance level, and verify the conditions for a one-sample z-test.
A focused answer to AP Statistics Topic 6.4, on writing the null and alternative hypotheses for a population proportion, choosing the significance level, and checking the random, large-counts (using the null value), and 10% conditions for a one-sample z-test.
9 min answer →

How do you state the hypotheses and check the conditions for a test comparing two proportions?

Topic 6.10 Setting Up a Test for the Difference of Two Population Proportions: state the hypotheses about the difference of two proportions, identify the significance level, and verify the conditions for a two-sample z-test using the pooled proportion.
A focused answer to AP Statistics Topic 6.10, on writing the hypotheses for a difference of two proportions, choosing the significance level, computing the pooled proportion, and checking the conditions for a two-sample z-test, with a worked set-up.
9 min answer →