KIN 4310 Lecture 13 Outline of Last Lecture I Formal Hypotheses II Type 1 and Type 2 Errors Outline of Current Lecture III Hypothesis Tests Current 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 H 0 is true 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 question o Therefore any difference between x and 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 value o Works for raw x scores or z scores o Always set cumulative to TRUE o NORMINV probability mean standard dev o Finds the value that has a given proportion of the area under the curve to the left of it o 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 hypothesis o Step 1 Calculate the t value o Step 2 After you know the t value you must determine the degrees of freedom df o Step 3 Determine the critical value of t o Step 4 Compare your t value to the critical value o Student s t test is used to determine if there is a significant difference between two groups 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 score o TTEST array1 array2 tails type o Returns the p value o Does the whole t test without even telling you what t is o Array1 is the first group s data o Array2 is the second group s data o 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 t 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