Practice Problems for Final Spring 2009 Chapter 10 A Determine whether each of the following is an example of an independent Completely Randomized Design or dependent Blocked Design study 1 The effectiveness of Prilosec for treating heartburn is tested by measuring gastric acid secretions in a group of patients treated with Prilosec and another group of patients given a placebo CRD 2 The effectiveness of Prilosec for treating heartburn is tested by measuring gastric acid secretions in each patient before and again after drug treatment BLOCK 3 The accuracy of verbal responses is tested in an experiment in which subjects report their weights verbally this weight is recorded and then the same person is weighed on a physician s scale and the actual weight is recorded for comparison BLOCK 4 The effect of a preservative as an ingredient is tested with a sample of cans of regular Coke and another sample of cans of diet Coke CRD B For the following decide the appropriate statistical test to analyze each data set Assume that data meet the assumptions of the test and use a 0 05 level of significance for each test 5 People in the United States spend a lot of money for the purchase of magnets to treat a variety of pains currently around 5 billion annually Researchers conducted a study to determine whether magnets are effective in treating back pain Pain was measured using a number scale People were randomly assigned to either the magnet treatment or a placebo treatment For each person the reduction in the amount of pain during the study was measured Did magnets reduce back pain for people Reduction in back pain for people given magnets mean 0 49 s 0 96 n 20 Reduction in back pain for people given placebos mean 0 44 s 1 4 n 20 a State the question ID the population Do magnets reduce back pain in this population b State your null and alternative hypotheses define symbols Ho Mu for magnets or Mu for placebo Ha Mu for magnets Mu for placebo where Mu is the population mean reduction in back pain c Analyze your data statistically 0 49 0 44 sqrt of 0 96 2 20 1 44 2 20 0 05 0 38 0 13 tcrit for 1 tailed test with df 19 1 729 d Provide a statement of conclusion that includes the statistical evidence and makes inference back to the population Magnets do not significantly reduce back pain compared to a placebo in this population t 0 13 p 0 05 n magnets n placebo 20 6 To look at the effectiveness of an SAT prep course at Washington High School 10 students were each given an SAT exam both before and after the prep course The data collected are presented below Is there sufficient evidence to conclude that the prep course improved the SAT score of people attending the class Student 1 2 3 4 5 6 7 8 9 10 SAT score after course DIFF AFTER BEFORE SAT score before course 20 720 700 0 840 840 10 820 830 40 900 860 30 870 840 10 700 690 30 800 830 20 1200 1180 20 950 930 10 1080 1070 Need to calculate the mean and std of the differences mean 11 s 20 2 a State the question ID the population Does the prep course significantly increase test scores in this population b State your null and alternative hypotheses define symbols Ho Mu difference or 0 Ha Mu differences is 0 where mu the population mean difference in test score calculated as the after course score the before course score c Analyze your data statistically 11 20 2 sqrt of 10 11 6 39 1 72 tcrit for 1 tailed test and 9 df 1 83 d Provide a statement of conclusion that includes the statistical evidence and makes inference back to the population This prep course does not significantly increase test scores in this population t 1 72 p 0 05 n 10 students Chapter 11 1 Blocking a will always increase your chances of rejecting the Ho when it should be rejected b c allows you to quantify the effect of the variable used in blocking d can allow a reduction in variability seen in experimental unit response to treatment effects is always made of blocks of size 2 2 Which of the following is true for a chi square test a It is used to compare 2 continuous numerical variables b c d The expected frequency number must be greater than 5 It analyzes data using a t test It is based on the chi square distribution which is a symmetric distribution 3 You set up an experiment There are 3 benches On each bench there are 4 flowerpots You assign 1 seed to each pot Each pot represents soil with a different type of fertilizer added When the study ends you will measure the height of every plant in your study Will this study use randomization or random sampling 4 Indicate which of the following would examples of a Completely randomized design CRD and which would be examples of a blocked design RBD a b experiment and habitat differences are expected BLOCK c There are 2 treatments and several sets of identical twins available for study BLOCK Although there is no prior knowledge about the study site the study is a field plot The available experimental units are homogeneous CRD 5 T or F The use of paired data often allows for the control of unmeasured or confounding variables because each pair is subjected to these confounding effects equally 6 If you ran a study using 20 experimental units in an unpaired experiment design What would be your degrees of freedom IF ASSUME THAT 2 TREATMENTS HAVE same n then a b c d 19 18 10 9 7 T or F The value of X2 can be negative zero or positive 8 T or F In the chi square test of independence data are classified according to 2 qualitative variables 9 T or F A hypothesis test involving a goodness of fit is always a left tailed test 10 T or F When using a chi square distribution in a hypothesis test for goodness of fit test the number of degrees of freedom is always the number of cells 11 T or F In the chi square test of independence the total number of observations in either both rows or else in both columns is set by the research