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AP Statistics Chapter 12: Significant Tests in Practice

12.1 – Tests about a Population Mean

Conditions for Inference about a Mean

• The data are a simple random sample (SRS) from the population of interest.

Normality

• Except in the case of small samples, the assumption that the data are an SRS from the population of interest is more important than the assumption that the population distribution is normal.

• Sample size less than 15. Use t procedures if the data are close to normal. If the data are clearly nonnormal or if outliers are present, do not use t.

• Sample size at least 15. The t procedures can be used except in the presence of outliers or strong skewness.

• Large samples. The t procedures can be used even for clearly skewed distributions when the sample is large, roughly n≥30.

Independence

• The population size is at least 10 times greater than the sample size

The One-Sample t Statistic and the t Distributions

Draw an SRS of size n from a population that has the Normal distribution with mean m and standard deviation s. The one-sample t statistic

has the t distribution with n-1 degrees of freedom.

The One-Sample t Test

To test the hypothesis Ho: mu = mu₀ based on an SRS of size n, compute the one-sample t statistic

Against either an alternate hypothesis of mu < mu_0, : mu > mu₀: or mu ≠ mu_0.

12.2 – Tests about a Population Proportion

Conditions for Inference about a Proportion

• The data are a simple random sample (SRS) from the population of interest.
• The population size is at least 10 times greater than the sample size
• Counts of expected successes and failures must be 10 or more.

Standard Error

When the standard deviation of a statistic is estimated from the data, the result is called the standard error of the statistic. The standard error of the sample proportion p-hat is

The One-Proportion z Procedures

To test the hypothesis Ho: p = p₀ based on an SRS of size n, compute the one-proportion z statistic

Against either an alternate hypothesis of p < p_0, : p > p₀: or p ≠ p_0.