 AP Statistics Section 12.1 A. Now that we have looked at the principles of testing claims, we proceed to practice. We begin by dropping the unrealistic.

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AP Statistics Section 12.1 A

Now that we have looked at the principles of testing claims, we proceed to practice. We begin by dropping the unrealistic assumption that we know the population standard deviation when testing claims about a population mean. As with confidence intervals, this leads to the use of ___ distributions when carrying out significance tests about.

One Sample t-Test Draw an SRS of size n from the population. The one-sample t statistic: has the t distribution with n – 1 degrees of freedom.

There is a slight change in the procedure for computing the p- value. The next examples show this change.

These P-values are exact if the population distribution is Normal and are approximately correct for large n in other cases.

Example: Is 98.6 o F Wrong? From a random sample of 106 people, the mean body temperature was 98.2 o F with a standard deviation of.6229. Test the common belief that the mean body temperature is 98.6 o F.

Parameter: The population of interest is all people. We wish to test Conditions:

Calculations: Interpretation:

If you were to choose a significance level for this test, what would it be? Why?

Describe a Type I and Type II error in this setting.

Construct a 99% confidence interval for the mean body temperature and interpret it.

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