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Unit 7: Inference for Quantitative Data: Means

10 dot points across 10 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you compute the t test statistic and P-value and conclude a test about a population mean?

Topic 7.5 Carrying Out a Test for a Population Mean: compute the t test statistic with n minus 1 degrees of freedom, find the P-value, compare to the significance level, and state a conclusion in context.
A focused answer to AP Statistics Topic 7.5, on computing the one-sample t statistic with n minus 1 degrees of freedom, finding the P-value, comparing to alpha, and stating a conclusion in context, with a full worked t-test.
11 min answer →

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

Topic 7.9 Carrying Out a Test for the Difference of Two Population Means: compute the two-sample (or paired) t test statistic, find the P-value, compare to the significance level, and state a conclusion in context.
A focused answer to AP Statistics Topic 7.9, on computing the two-sample t statistic with the unpooled standard error (or the paired one-sample t statistic on differences), finding the P-value, and concluding in context, with a full worked test.
11 min answer →

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

Topic 7.6 Confidence Intervals for the Difference of Two Means: check the conditions and construct a two-sample t-interval for the difference between two population means, including the paired case, using the unpooled standard error.
A focused answer to AP Statistics Topic 7.6, on building a two-sample t-interval for the difference of two population means and distinguishing it from a paired (one-sample) interval, with a full worked interval.
11 min answer →

How do you construct a confidence interval for a population mean using the t-distribution?

Topic 7.2 Constructing a Confidence Interval for a Population Mean: check the conditions and construct a one-sample t-interval for a population mean, using the t critical value, the standard error, and the correct degrees of freedom.
A focused answer to AP Statistics Topic 7.2, on building a one-sample t-interval for a population mean - checking conditions, finding the t critical value with n minus 1 degrees of freedom, the standard error, and the margin of error - with a full worked interval.
11 min answer →

Why is there always uncertainty when estimating a population mean from a sample, and how does inference account for it?

Topic 7.1 Introducing Statistics: Should I Worry About Error?: explain why a sample mean varies from sample to sample, why this sampling variability creates uncertainty about the population mean, and how inference quantifies that error.
A focused answer to AP Statistics Topic 7.1, on why a sample mean varies, why that sampling variability creates unavoidable uncertainty about the population mean, and how confidence intervals and tests quantify the error.
9 min answer →

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

Topic 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval: use a one-sample mean interval to judge whether a claimed mean is plausible, and explain how confidence level and sample size affect the interval.
A focused answer to AP Statistics Topic 7.3, on using a one-sample t-interval to judge whether a claimed value of the population mean is plausible, and explaining how confidence level and sample size change the interval, with worked justifications.
9 min answer →

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

Topic 7.7 Justifying a Claim About the Difference of Two Means Based on a Confidence Interval: use a two-sample (or paired) mean interval to judge whether the means differ and to assess claims about the size and direction of the difference.
A focused answer to AP Statistics Topic 7.7, on using a two-sample or paired mean confidence interval to judge whether two means differ and to assess claims about the size and direction of the difference, with worked justifications.
9 min answer →

How do you select, implement, and communicate the correct inference procedure for a given scenario?

Topic 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures: identify the appropriate confidence interval or significance test for a scenario (proportion or mean, one or two samples, paired or independent), and carry it out and communicate the result correctly.
A focused answer to AP Statistics Topic 7.10, on choosing the correct inference procedure (proportion vs mean, one vs two samples, paired vs independent, interval vs test) for a scenario and implementing and communicating it correctly, with a worked decision and procedure.
11 min answer →

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

Topic 7.4 Setting Up a Test for a Population Mean: state the null and alternative hypotheses about a population mean, identify the significance level, and verify the conditions for a one-sample t-test.
A focused answer to AP Statistics Topic 7.4, on writing the null and alternative hypotheses for a population mean, choosing the significance level, and checking the random, normal/large-sample, and 10% conditions for a one-sample t-test.
9 min answer →

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

Topic 7.8 Setting Up a Test for the Difference of Two Population Means: state the hypotheses about the difference of two means, decide between a two-sample and a paired procedure, identify the significance level, and check the conditions.
A focused answer to AP Statistics Topic 7.8, on writing the hypotheses for a difference of two means, deciding between a two-sample and a paired t-test, choosing the significance level, and checking the conditions.
9 min answer →