Answer :

Final answer:

When testing a population mean, we use a Test Statistic, generally a t-score. In AP Statistics exams, a formula for this is usually provided. The p-value, which represents the probability of obtaining the observed test statistic, can easily be calculated using a statistical calculator or computer.

Explanation:

When testing a population mean, we often use a Test Statistic. This is an estimated value from the sample data that is used to decide whether our null hypothesis should be rejected. The type of test statistic used often depends on the circumstances, but generally a t-score is used when we're dealing with small sample sizes and don't know the population standard deviation.

For example, consider a test comparing two independent population means with unknown and possibly unequal population standard deviations, called the Aspin-Welch t-test. Here, the degrees of freedom, which determine the shape of the t-distribution used in the test, are calculated using a formula developed by Aspin-Welch.

In an AP Statistics exam, a formula for calculating this test statistic should be provided. However, statistical calculators and computers can easily calculate the associated probabilities, which are known as the p-value. The p-value basically tells us the probability of obtaining the observed test statistic (or one even more extreme), assuming the null hypothesis is true.

Learn more about Test Statistic here:

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