FANR 3000 1st Edition Lecture 9Outline of Last Lecture I. HypothesesII. Type I and Type II ErrorsIII. P-values Outline of Current Lecture I. Hypothesis Testing II. T-TestsIII. Types of T-tests Current LectureI. Hypothesis Testing- Comparing 2 populations1) Determine null (H0) and alternative (H1) hypotheses 2) Specify level of significance (α, probability of Type I error) 3) Select the test statistic that will be used 4) Collect the sample data and compute the value of the test statistic 5) 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- α 1) Allowable error 2) The level of significance (p-value < α 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 α5) The smaller the value of α, the more difficult it is to reject H06) Test results are “stronger” with a lower αII. 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 random2. 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 hypothesesa. When testing differences between means, the null hypothesis is that the difference between means is some specified value (usually zero)2. Choose a significance level (α )3. Select the test statistic that will be used (difference between sample means)4. Collect sample data from both populations5. Execute the test statistic III. 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 mean2. 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