AP Statistics NAME:

Exam Review: Strand 4: Statistical Inference Date: Block:

IV. Statistical Inference:

(30%-40%)

Statistical inference guides the selection of appropriate models.

1. Estimation (point estimators and confidence intervals)

1. Estimating population parameters and margins of error

2. Properties of point estimators, including unbiasedness and variability

3. Logic of confidence intervals, meaning of confidence level and confidence

intervals, and properties of confidence intervals

4. Large sample confidence interval for a proportion

5. Large sample confidence interval for a difference between two proportions

6. Confidence interval for a mean

7. Confidence interval for a difference between two means

(unpaired and paired)

8. Confidence interval for the slope of a least-squares regression line

2. Tests of significance

1. Logic of significance testing, null and alternative hypotheses; p-values; one-

and two-sided tests; concepts of Type I and Type II errors; concept of

power

2. Large sample test for a proportion

3. Large sample test for a difference between two proportions

4. Test for a mean

5. Test for a difference between two means (unpaired and paired)

6. Chi-square test for goodness of fit, homogeneity of proportions, and

independence (one- and two-way tables)

7. Test for the slope of a least-squares regression line

You need to know the appropriate statistical inference procedure to use in a given situation.

On any hypothesis testing problem:

1. State hypotheses in words and symbols.

2. Identify the correct inference procedure and verify conditions for using it.

3. Calculate the test statistic and the P-value (or rejection region).

4. Draw a conclusion in context that is directly linked to your P-value or rejection region.

State your hypotheses in terms of population parameters:

µ: population mean or p: population proportion, NOT sample statistics

It is not enough to state the conditions for the chosen inference procedure. You must

show that the conditions are satisfied.

On any confidence interval problem:

1. Identify the population of interest and the parameter you want to draw conclusions

about.

2. Choose the appropriate inference procedure and verify conditions for its use.

3. Carry out the inference procedure.

4. Interpret your results in the context of the problem.

Type I Error: Rejecting a null hypothesis that is true –

P(Type I error) = α = significance level

Type II Error: Accepting a null hypothesis that is false

Power of a Test: Probability of correctly rejecting a null hypothesis –

Power= 1 – P(Type II Error)

Increase the power of a test by

increasing the sample size OR increasing the significance level.

Null Hypothesis (H0) Actually

Your Decision

True False

Don’t Reject H0 Correct Type II Error

Reject H0

Type I Error Correct

Power = 1 –

P(Type II Error)

Power = the probability of correctly rejecting a false hypothesis

Practice Questions

The table below lists the different inference procedures you should know for the AP exam. In

each of the scenarios below, choose the correct inference procedure.

1. Which brand of AA batteries last longer—Duracell or Eveready?

2. According to a recent survey, a typical teenager has 38 contacts stored in his/her cellphone.

Is this true at your school?

3. What percent of students at your school have a MySpace page?

4. Is there a relationship between the age of a student’s car and the mileage reading on the

odometer at a large university?

5. Is there a relationship between students’ favorite academic subject and preferred type of

music at a large high school?

6. Who is more likely to own an iPod—middle school girls or middle school boys?

7. How long do teens typically spend brushing their teeth?

8. Are the colors equally distributed in Fruit Loops?

9. Which brand of razor gives a closer shave? To answer this question, researchers recruited

25 men to shave one side of their face with Razor A and the other side with Razor B.

10. How much more effective is exercise and drug treatment than drug treatment alone at

reducing the incidence of heart attacks among men aged 65 and older?

AP Statistics NAME:

Exam Review: Statistical Inference Practice Date: Block:

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