Stat 301 Review Test 2 Below is a table of the tests that we covered in chapters 6 7 12 and 13 You will need to know the following for each of the tests 1 Given a problem which test should be used 2 How to write the hypotheses for the problem 3 How to calculate and or read the test statistic from the printout 4 How to calculate and or read the P value from the printout 5 What conclusions should be drawn Type of test 1 sample z test When is it used One set of data is known Quantitative data Confidence interval x z Hypothesis test procedure Hypotheses H0 n To find the z value look at the last row of the t table versus 0 Ha 0 Ha Test Statistic x 0 z 0 or H a 0 n 1 sample t test One set of data is unknown Quantitative data Find the confidence interval from SPSS printout be sure to add in the test value OR x t s n To find the t value look at the n 1 degrees of freedom row on the t table Matchedpairs Values are matched Either both measurements are recorded on the same unit or a before after study is conducted Quantitative data Find the confidence interval from SPSS printout OR xdiff t sdiff n To find the t value look at the n 1 degrees of freedom row on the t table P value Ha 0 use P Z z Ha 0 use P Z z or Ha 0 use 2P Z z Look up P values on TABLE A Hypotheses H0 0 versus Ha 0 Ha 0 or H a Test Statistic x 0 OR read SPSS printout t s n P value P T t Ha 0 use Ha 0 use P T t or Ha 0 use 2P T t 0 Look up P values on the t table df n 1 OR read SPSS printout Hypotheses H 0 diff 0 versus Ha diff 0 Ha diff 0 or H a diff Test Statistic xdiff 0 t OR read SPSS printout sdiff n P value H a diff 0 use P T t Ha diff 0 use P T t or Ha diff 0 use 2P T t Look up P values on the t table df n 1 OR read SPSS printout 1 0 2 sample t test Data comes from two independent samples selected from two independent populations or a completely randomized experiment with two factor levels or treatments Quantitative data Find the confidence interval from the SPSS printout OR x1 x2 t s12 n1 s22 n2 To find the t value look at the smaller of n1 1 and n2 1 degrees of freedom row on the t table Hypotheses H0 1 2 versus Ha 1 2 Ha 1 2 or H a 1 Test Statistic x1 x2 OR read SPSS printout t s12 s22 n1 n2 P value Ha 1 2 use P T t Ha 1 2 use P T t or 1 2 use 2P T t Ha 2 Look up P values on the t table OR read SPSS printout One way ANOVA Data comes from more than two independent samples or from an experiment with one factor with multiple levels of that factor Quantitative data None Hypotheses H0 1 2 H a not all the 3 I I s are the same Test statistic Read F from the SPSS printout P value Read P value from the SPSS printout Further analysis If you reject the null hypothesis further analysis is necessary to determine which means are different Bonferroni s procedure is one possibility Appropriate if 2 smallest s largest s Two way ANOVA Compares the means of populations that are classified two ways or the mean response in a two factor experiment Quantitative data None Hypotheses H 0 main effect of A is zero H a main effect of A is not zero H 0 main effect of B is zero H a main effect of B is not zero H 0 interaction between A and B is zero H a interaction between A and B is not zero Test statistics Read F from the SPSS printout P value Read P value from the SPSS printout 2 There are some additional concepts that you will need to understand They are listed below 1 Assumptions that need to be met in order to perform the following tests or calculate the confidence intervals 2 How robust the tests above are to the assumption of normality with respect to the sample size 3 Whether the test you are performing is reasonable considering the distribution of your data and your sample size 4 The relationship between confidence intervals and two sided tests and when a confidence interval can be used to draw conclusions regarding a hypothesis test 5 How large a sample is needed to gain a certain margin of error in a one sample Z test 6 Know how to test the standard deviations to see if it is OK to pool the variances in both the one and two way ANOVAs 7 Calculate R 2 and the estimate for 8 When it is better to calculate a confidence interval versus conduct a hypothesis test 9 Determine which means are different in ANOVA given the SPSS printout in Bonferroni s procedure 10 Be able to describe and interpret side by side boxplots and plots of means for the oneway and two way ANOVAs 11 Know how the two way ANOVA is different from the one way ANOVA and two sample comparison of means 12 Know how to recognize the response variable factors number of levels for each factor and the total number of observations 13 Be able to interpret the appropriate graphs for both one way and two way ANOVAs The following problems have been taken from old tests 3 Problems 1 4 are multiple choice There may be more than one correct answer for each question Circle ALL answers which are correct 1 Circle the letter of the following methods that would decrease the width of a confidence interval for a mean if all else stays the same a Increase the sample size b Decrease the sample size c Increase the level of confidence d Decrease the level of confidence e None of the above 2 A 95 confidence interval indicates that a 95 of the intervals constructed using this process based on same sized samples from this population will include the population mean b 95 of the time the interval will include the sample mean c 95 of the possible population means will be included by the interval d 95 of the possible sample means same size samples will be included by the interval e None of the above 3 Which of the following is true if your P value is 0 01 and your is 0 05 a You reject Ha b You do not reject Ha c Your results are significant d Your results are not significant e None of the above 4 John took a simple random sample of 25 lemon drop packs from …