Quiz 6 November 4, 2005 Name ANSWER KEYStat 217 Cocaine addiction is hard to break. Addicts need cocaine to feel any pleasure, so therapists give them an antidepressant drug to help. A 3 year study with 72 chronic cocaine users compared two antidepressant drugs, a new drug called desipramine, and lithium, the standard drug used to treat cocaine addition. In addition, some addicts were given a placebo (or dummy) drug. 72 addicts were randomly assigned to each of these treatments. The results are given in the following 2-way table: Cocaine RelapseYes No TOTALSdesipramine10 14 24lithium 18 6 24placebo 20 4 24TOTALS 48 24 721. What percentage of all addicts relapsed back to cocaine use after treatment?48/72 = 67%2. What percentage of all addicts took the placebo?24/72=33%3. Why is it important that placebo or dummy pills were used in the study?Placebo pills were included in the study so that we could compare the results of the drugs to a “control.”4. Which treatment appears to be most effective for cocaine addiction? Give the proportions you are using to answer this question.Desipramine has 14/24=58% success (no cocaine relapse) compared to 6/24=25% for lithium users and 4/24=17% for placebo users.5. Give a possible lurking variable that might change the direction of your assertion in #5.Perhaps the therapists who administered the desipramine were more effective than the therapists administering the other drug.Here is the original 2-way table of drug treatment and cocaine relapse from the other side of the quiz, as well as some handy dandy formulas: cellsallectedecte dobservedXexpexp22 ,   11  cr , ntotalcolumntotalrow ))((6. Fill in the following table with the missing expected cell counts. SHOW YOUR WORK! Cocaine RelapseYes Nodesipramine 16 8lithium 16 8placebo 16 8since (row total)(col total)/n = (24)(24)/72 = 87. Let us test whether there is an association between drug and cocaine relapse. (a) What are the null and alternative hypotheses being tested?H0: There is no association between drug and cocaine relapseHa: There is an association between drug and cocaine relapse(b) Fill in the missing contributions to the test statistic. SHOW YOUR WORK! Cocaine RelapseYes Nodesipramine 2.25 4.5lithium .25 .5placebo 1 2since (obs – exp)2/exp = (20 – 16)2/16 = 1.(c) Calculate the value of the test statistic. SHOW YOUR WORK!X2 = 2.25 + 4.5 + .25 + .5 + 1 + 2 = 10.5(d) Give the distribution of the test statistic.X2 ~2(2), where the degrees of freedom is 2 since (r-1)(c-1) = (3-1)(2-1) = 2(e) If the p-value is .005, then make a decision at the 0.05 significance level. Since the p-vaue=.005<.05 = significance level, then we REJECT H0.(f) State your conclusion in terms of this problem.The evidence suggests that there is an association between drug and cocaine relapse.(g) If there is an association, then which drug treatment group(s) have higher or lower incidences of cocaine relapse than the others? Indicate which output you are using to justify your answer.Since the contribution to the test statistic of 4.5 is the largest, then we have we have a larger incidence of addicts taking desipramine who are not relapsing than the other treatments. Cocaine RelapseYes No TOTALSdesipramine 10 14 24lithium 18 6 24placebo 20 4 24TOTALS 48 24