[Latexpage]
Instructions for using the various graphing calculators are linked in this post.
Here is how hypothesis testing works for the t-test on the mean:
We first state our null hypothesis and alternative hypothesis.
For this type of test, the null hypothesis always has an = sign in it:
$H_{0}: \mu = \mu_{0}$
The alternative can have any one of three forms, depending on what is important to distinguish. Either $H_{a}: \mu \neq \mu_{0}$
or $H_{a}: \mu < \mu_{0}$
or $H_{a}: \mu > \mu_{0}$
Where $\mu_{0}$ is a number (the hypothesized value of the population mean).
Using the t.test function in R, or the t-test on your calculator, the information we get includes p-values.
A p-value measures the strength of the evidence (the sample data) against the null hypothesis. Here is another source that explains more about p-values. The smaller p is, the more sure we are that we should reject the null hypothesis.
In practice, we choose a value of $\alpha$, called the level of significance of the test. It represents the probability of making a Type I error. (Usually that means we want $\alpha$ to be small, 5% or less.) Then we look at the p-value returned by R or by the calculator. If $p \le \alpha$ we will reject the null hypothesis: otherwise, we accept the null hypothesis or reserve judgement.
Here are problems to practice deciding what form of the alternative hypothesis to use: (we did some of them in class)
Math2501HypothesisTestingProblems
Here are problems to practice using the t-test and drawing conclusions from it: #4-5 and 8-11 especially
