Chi-Square TestChi-Square TestChi-Square TestIn-class Work on 2 Tests ANSWER KEY1. A survey is undertaken to determine the incidence of alcoholism in different professional groups. Random samples of clergy, educators, executives, and merchants were interviewed by a team of sociologists. The 2-way table with the results was given in the last in-class work. The sociologists conducting the study wish to test if any of the professions have a significantly different incidence of alcoholism than the others.(a) What are the null and alternative hypotheses being tested?H0: There is no association between alcoholism and professionHa: There is an association between alcoholism and profession(b) Fill in the following table with the EXPECTED CELL COUNTS: Alcoholic NonalcoholicClergy 58.25 241.75Educators 48.54 201.46Executives 58.25 241.75Merchants 67.96 282.04(c) Fill in the following table with the “contributions” to the test statistic X2 : Alcoholic NonalcoholicClergy 11.829 2.85Educators .124 .03Executives 1.314 .317Merchants 3.329 .802(d) Use the table in (c) to calculate the test statistic X2 . X2 = 20.597(e) What is the distribution of the test statistic X2 ? 2(3)(f) What is the p-value? 0.000 (g) Make a decision at the 0.05 significance level. REJECT H0(h) State your conclusion in terms of this problem.The evidence suggests that there is an association between alcoholism and profession.(i) Describe the association in terms of this problem. That is, which professional groups have higher or lower incidences of alcoholism than the others?Since the chi-square contributions of 11.829 and 3.329 are large compared to the other contributions, then the cells associated with these large contributions account for the significant association. Thus, clergy have a significantly lower incidence of alcoholism than the other professions, and merchants have a significantly higher incidence of alcoholism than the others. 2. A study was conducted to explore the association between a child’s birth order and the occurrence of juvenile delinquent behavior. The subjects were a random sample of girls enrolled in public high schools in a large city. Thedata were analyzed in MINITAB and the output appears below. NOTE: some output has been purposely deleted.Chi-Square TestExpected counts are printed below observed counts Always Sometimes Never TotalOldest 24 55 230 30937.12 78.92 192.96 In-between 29 61 186 276 33.16 70.49 172.35 Youngest 35 89 122 246 29.55 _____ 153.62 Only child 23 31 39 93 11.17 23.75 58.07Total 111 236 577 924Chi-Sq = 4.637 + 7.251 + _____ + 0.521 + 1.279 + 1.081 + 1.004 + 10.899 + 6.507 + 12.522 + 2.211 + 6.265 = 61.289DF = ________, P-Value = 0.000 (a) What are the null and alternative hypotheses being tested? H0: There is no association between occurrence of juvenile delinquence and a child’s birth orderHa: There is an association between occurrence of juvenile delinquence and a child’s birth order(b) Calculate the expected count for the “Youngest” and “Sometimes” cell . (246*236)/924=62.83(c) Calculate the contribution to the test statistic for the “Oldest” and “Never” cell.(obs – exp)2/exp = (230- 192.96)2/192.96 = 7.1101(d) What is the value of the test statistic X2 ? 61.289 (e) What is the distribution of the test statistic X2 ? 2(6)(f) What is the p-value? 0.000(g) Make a decision at the 0.05 significance level. REJECT H0(h) State your conclusion in terms of this problem. The evidence suggests that there is an association between occurrence of juvenile delinquence and a child’s birth order(i) Describe the association in terms of this problem. The oldest children tend to have less occurrences of delinquent behavior than other children (since all of the chi-square contributions for ‘older’ are large) , while children with no siblings tend to always have delinquent behavior more than other children (since all of the chi-square contributions for ‘only child’ are large)3. Use the following output of a2test performed in MINITAB to determine whether there is an association between a child’s gender and the child’s primary interests (grades, being popular, or sports) for middle-school children in a large city.(a) What are the null and alternative hypotheses being tested? H0: There is no association between gender and a child’s primary interestHa: There is an association between gender and a child’s primary interest(b) Make a decision at the 0.05 significance level. Since X2 = 89.966 and p-value=0.000 < .05, then we REJECT H0(c) State your conclusion in terms of this problem. The evidence suggests that there is an association between gender and a child’s primary interest(d) Describe the association in terms of this problem. Boys have more of an interest in sports and less of an interest in grades than girls; or, you can say thatgirls have less of an interest in sports and more of an interest in grades than boys.(e) Give a possible confounding variable which might lead to Simpson’s Paradox.The economic status of the child’s family.4. Here the 2Test is looking for an association between how many parents smoke (both, one, or none) and whether or not their child smokes.(a) What are the null and alternative hypotheses being tested? H0: There is no association between how many parents smoke and whether or not their child smokesHa: There is an association between how many parents smoke and whether or not their child smokes(b) Make a decision at the 0.05 significance level.Since X2 = 37.566 and p-value=0.000 < .05, then we REJECT H0(c) State your conclusion in terms of this problem. The evidence suggests that there is an association between how many parents smoke and whether or not their child smokesChi-Square TestExpected counts are printed below observed counts Grades Popular Sports Total Boys 96 32 94 222 144.19 28.40 49.42Girls 295 45 40 380 246.81 48.60 84.58Total 391 77 134 602Chi-Sq = 16.105 + 0.458 + 40.226 + 9.409 + 0.267 + 23.501 = 89.966DF = 2, P-Value = 0.000Chi-Square TestExpected counts are printed below observed counts Smokes