Question

How are the smoking habits of students related to the smoking habits of their close family members? Here is a two-way table from a survey of male students in six secondary schools in a certain country. At Least One Close Family Member Smokes No Close Family Member Smokes Student Smokes 116 Student Does Not Smoke 205 75 As you can see, there is an association between smoking by close family members and smoking by high school students. The students are more likely to smoke if a close family member smokes. We want to know whether this association is statistically significant. (a) State the hypotheses for the chi-square test. What do you think the population is? O Ho: There is no association between whether the student smokes and whether close family members smoke. H. There is a negative association between whether the student smokes and whether close family members smoke. O Hi There is some association between whether the student smokes and whether close family members smoke. H: There is no association between whether the student smokes ar etween whether the student smokes and whether close family members smoke. Hp: There is a negative association between whether the student smokes and whether close family members smoke. H. There is no association between whether the student smokes and whether close family members smoke. • Hi There is no association between whether the student smokes and whether close family members smoke. H. There is some association between whether the student smokes and whether close family members smoke. (b) Find the expected cell counts. (Round your answers to three decimal places.) Student Smokes Student Does Not Smoke At Least One Close Family Member Smokes No Close Family Member Smokes Write a sentence that explains in simple language what "expected counts" are. These are the counts we would expect-except for random variation-if H, were true. These are the counts we would expect-except for random variation-if Ho were true. These are the counts we would expect-except for random variation-if the distribution was Normal. These are the counts we would expect-except for random variation-if the sample size was very large. These are the counts we would expect-except for random variation-if the hypothesis test was significant. (c) Find the chi-square statistic and its degrees of freedom. (Round your chi-square statistic to three decimal places.) x2 = df = What is your conclusion about significance? (Use this table of significance levels.) This result is significant at 10% but not 5%. This result is significant at 5% but not 1%. O This result is significant at 1% but not 0.1%. This result is significant at 0.5% but not 0.1%. O This result is significant at 0.1% but not 0.01%.

Answer 1

Ans: a) top toon 4 correct student smokes student does not smokes 107.508 23,492 Atleast one class family member Smokes No close family member 33.492 66.508 Smokes Expected cell Count you dodal & Column total Grand total - these are the counts we would expect except for random varration - Of Ho were true 1 c o E (0-c)?/ 116 107.508 0.67 205 213.492 0.34 25 33.492 2.15 75 66.568 1.08 22 - E 16-c)2 ) - 0.67 +0.36+2.1571 - 24.246 df = (8-1)-(C-1) = (2-1) + (2-1) = [1] c) P-value = 0.0525 P-value Za (0.1) and p-value 2 (0.05). The result Signaficant at lot, but not 5 do