FANR 3000 1st Edition Lecture 9 Outline of Last Lecture I Hypotheses II Type I and Type II Errors III P values Outline of Current Lecture I Hypothesis Testing II T Tests III Types of T tests Current Lecture I Hypothesis Testing Comparing 2 populations 1 2 3 4 5 II Determine null H0 and alternative H1 hypotheses Specify level of significance probability of Type I error Select the test statistic that will be used Collect the sample data and compute the value of the test statistic Use the value of the test statistic to make a decision using a rejection point Zc tc or a p value 6 Interpret statistical results in real world terms 1 Allowable error 2 The level of significance p value denotes significant results 3 Acceptable probability of a Type I Error 0 01 0 10 4 the location of the rejection boundary is a function of 5 The smaller the value of the more difficult it is to reject H0 6 Test results are stronger with a lower T Tests A 2 sample t test is appropriate ONLY if the samples meet the following criteria 1 2 samples one from each population are independent and random 2 Both populations are approximately normally distributed These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Compare 2 means using a new sampling distribution the sampling distribution for the difference in means o To determine if the samples come from the same population The larger the difference the larger the calculated t score so the further out in the tail the calculated t score will be 1 Determine Null and Alternative hypotheses a When testing differences between means the null hypothesis is that the difference between means is some specified value usually zero 2 3 4 5 III Choose a significance level Select the test statistic that will be used difference between sample means Collect sample data from both populations Execute the test statistic Types of T tests 1 One sample t test trying to determine if there is a difference in the population mean calculated from your samples against the hypothesized population mean 2 Two sample t test to determine if there is a difference in the population mean between the two groups you have sampled For equal or unequal variance 3 Paired sample t test to determine differences between populations when you have paired samples When you have similar sample individuals each receiving a different treatment or when the same sample individual is in the first treatment control and then is subjected to the second treatment For t values if we calculate a t value that is greater than our critical t value then the two populations are statistically different For p values if we calculate a p value less than our alpha value then we assume the two populations to be statistically different