Lecture 13Outline of Last Lecture I. Formal HypothesesII. Type 1 and Type 2 ErrorsOutline of Current Lecture III. Hypothesis TestsCurrent Lecture- Determine a test statistic, use an appropriate statistical method to test the hypothesis, two possible outcomes (reject H0 or fail to reject H0)- Critical Value Method: Based on a statistical model, find a value that partitions 95% of the “usual” values from 5% of the “unusual” values- P-Value Method: The probability of getting your test statistic or one more extreme if H0 istrue- One-sample Z test: A special hypothesis test for comparing a sample to a population; Requires a priori knowledge of the population mean (e.g., census data)o Assume H0. The sample was randomly selected from the population in questiono Therefore, any difference between x and µ is due to random effects (sampling error)o What is the probability of getting a difference equal to or more extreme than our data?o If the null hypothesis is true, z has a normal distribution- Normal Distribution (EXCEL)o NORMDIST(x,mean,standard_dev,cumulative)o Finds area under the curve to the left of a given valueo Works for raw x scores or z-scoreso Always set cumulative to TRUEo NORMINV(probability,mean,standard_dev)o Finds the value that has a given proportion of the area under the curve to the left of ito Useful for finding critical values- The t-test: A special hypothesis test that is used to determine if there is a significant difference between two groups; Like all hypothesis tests, a t-test will tell you whether or not you should reject the null hypothesiso Step 1: Calculate the t-valueo Step 2: After you know the t-value, you must determine the degrees of freedom (df)o Step 3: Determine the critical value of to Step 4: Compare your t-value to the critical valueo Student’s t-test is used to determine if there is a significant difference between two groupsKIN 4310- T-Test (EXCEL)o TINV(alpha,deg_freedom)o Returns the critical t-score for a given o Only works for two-tailed tests!o Always gives a positive t-scoreo TTEST(array1, array2, tails, type)o Returns the p-valueo Does the whole t-test without even telling you what t iso Array1 is the first group’s datao Array2 is the second group’s datao Tails is the number of tails (1 or 2)o Type is the type of t-Test 1 = t-Test for dependent means 2 = t-Test for independent means (equal variance) 3 = t-Test for independent means (unequal variance)o TDIST(t, deg_freedom, tails)o Returns the area in the tail(s) beyond tThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used asa supplement to your own notes, not as a