The idea behind the paired t-test is to reduce this two-sample situation, where we are comparing two means, to a single sample situation where we are doing inference on a single mean, and then use a simple t-test that we introduced in the previous module.

1.how do you put it into one simple comparison? ( you take Miu 1- miu2. this will give the difference which then can be used to see the true value.

2. you wil then you use the difference to find the T statistic. there are 4 steps.

1.insead of Mo you will now Use Md ( mean difference)

2.Checking Conditions and Calculating the Test Statistic

a. random samples

b. Normal or larg sample size

3. replace x-bar with Xbar(d) and replace s with S(d) in the t equation.

4. find the P value

p-value tells us that there is very little chance of getting data like those observed (or even more extreme) if the null hypothesis were true.

5. conclusion in context

If the p-value is small, there is a significant difference between what was observed in the sample and what was claimed in Ho, so we reject Ho and conclude that the categorical explanatory variable does affect the quantitative response variable as specified in Ha. If the p-value is not small, we do not have enough statistical evidence to reject Ho. In particular, if a cutoff probability, α (significance level), is specified, we reject Ho if the p-value is less than α. Otherwise, we do not reject Ho.

Typically, as in our example, one of the measurements occurs before a treatment/intervention (2 beers in our case), and the other measurement after the treatment/intervention. ;