These are statistics that come from "eitheror" populations. The proportion of people who smoke. The proportion of people who are Democrats, etc. The value of the proportion always falls between zero and one.
 the sample mean is p^ (meaning "phat").
 The sample standard error, s_{e}, is the square root of [p^(1p^)/n]

These are statistics that come from populations where the numbers have a scale, such as inches or milesperhour or score on a test. The value can be anythingit does not have to fall between zero and one.
 the sample mean is X.
 The sample standard error, s_{e}, is the square root of [S(X_{i}  X)^{2}/(n1)]

 Obtain z* based on confidence level
 Multiply z* by s_{e} to get the margin of error, m.
 The confidence interval goes from p^  m to p^ + m

 If alternative hypothesis is "not equal to" (i.e., a 2tailed test), then use the significance level, a/2, to select z*. Otherwise, use just a
 In a onesample test, calculate z by taking the value of p^ minus its value under the null hypothesis and dividing by s_{e}. If z is larger than z* (larger could mean more negative if z* is negative), then reject the null hypothesis
 In a twosample test, then the test statistic looks something like (p^_{1}  p^_{2})/[square root of
(s_{e1})^{2} +
(s_{e2})^{2}]

 df = n1 (degrees of freedom)
 Obtain t* based on confidence level and df
 Multiply t* by s_{e} to get the margin of error, m.
 The confidence interval goes from X  m to X + m

 If alternative hypothesis is "not equal to" (i.e., a 2tailed test), then use the significance level, a/2, to select t* (you also need to use the degrees of freedom) or to compare with the Pvalue. Otherwise, use just a
 In a onesample test, calculate t by taking the value of X minus its value under the null hypothesis and dividing by s_{e}. If t is larger than t* (larger could mean more negative if z* is negative), then reject the null hypothesis
 In a twosample test, use a calculator. Since we never obtain t* in this process, we can use the Pvalue to decide whether or not to accept or reject. When the Pvalue is lower than a (or a/2 with a twosided alternative hypothesis), we reject the null hypothesis.
