Appendix C. Assumptions and Conditions for Inference

The following are the assumptions and conditions essential for proper statistical inference. Be sure that you know and understand all of the assumptions and conditions for the various types of confidence intervals and tests. Make certain that you check them accordingly when conducting inference on the AP Exam. It will be assumed that you know that the assumptions and conditions should always be checked when doing inference. The test questions about inference will probably not remind you to check them.

One-sample t-interval or one-sample t-test

Assumptions

1. Individuals are independent

Conditions

1. SRS and <10% of population (10n<N)

2. Normal population assumption

2. One of the following:

  • Given a normal population

  • Graph of data is symmetric with no outliers

  • Sample is large enough (n ≥ 30) that the sampling distribution of One-sample t-interval or one-sample t-test is approximately normal

Remember that matched pairs are a one-sample t-procedure. Check the assumptions and conditions for a one-sample t-procedure when doing matched pairs. You should also be sure to state that the “data are matched,” as this is an added assumption.

Two-sample t-interval or two-sample t-test

Assumptions

1. Samples are independent of each other

Conditions

1. Are they? Does this seem reasonable?

2. Individuals in each sample are independent

2. Both SRSs and both <10% population (10n<N for both samples)

3. Normal populations assumption

3. One of the following:

  • Given normal populations

  • Graph of data for both samples shows no outliers or strong skewness

  • Samples are both large (n ≥ 30); therefore the sampling distribution of Two-sample t-interval or two-sample t-test1 − Two-sample t-interval or two-sample t-test2 is approximately normal

One-proportion z-interval or test

Assumptions

1. Individuals are independent

Conditions

1. SRS and n < 10% of population

2. Sample is large enough

2. np ≥ 10 and n(1 − p) ≥ 10 Use One-proportion z-interval or test for C.I. and p0 for Tests

Two-proportion z-interval or test

Assumptions

1. Samples are independent of each other

Conditions

1. Is this reasonable?

2. Individuals in each sample are independent

2. Both samples are SRSs and n < 10% of population for both samples

3. Both samples are large enough

3. np ≥ 10 and n(1 − p) ≥ 10 for both samples

Chi-square goodness of fit (one variable from one sample)

Assumptions

1. Data are in counts

Conditions

1. Is this true?

2. Data are independent

2. SRS and <10% of population (10n<N)

3. Sample is large enough

3. All expected counts ≥ 5

Chi-square test for homogeneity (samples from many populations)

Assumptions

1. Data are in counts

Conditions

1. Is this true?

2. Data in each sample are independent

2. SRSs and each sample <10% of population (10n<N)

3. Samples are large enough

3. All expected counts ≥ 5

Chi-square test for independence/association (one sample from one population classified on two variables)

Assumptions

1. Data are in counts

Conditions

1. Is this true?

2. Data are independent

2. SRS and <10% of population (10n<N)

3. Sample is large enough

3. All expected counts ≥ 5

Regression (t)

Assumptions

1. Relationship has linear form

Conditions

1. Scatterplot is approximately linear

2. Residuals are independent

2. Residual plot does not have a definite pattern

3. Variability of residuals is constant

3. Residual plot has even spread

4. Residuals are approximately normal

4. Graph of residuals is approximately symmetrical and unimodal, or normal probability plot is approximately linear

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