Assume that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. Use the sign test with a 0.05 significance level to test the null hypothesis of no difference. Positive signs: 856; negative signs: 151; ties: 57 (from a Pew Research Center poll of adults who were asked if they know what Twitter is)

Solution 7BSC Step 1 By assuming that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. We use the sign test with a 0.05 significance level to test the null hypothesis of no difference. The Hypotheses can be expressed as H0 There is no difference between adults who know what Twitter is and those who do not know. H : There is a difference between adults who know what Twitter is and those who do not 1 know. We know that, Positive signs = 856 Negative signs = 151 Number of ties = 57 Now, the Test Statistic is the less frequent sign i.e., negative sign = 151 Therefore, x = 151 is the required value of test statistic. Hence for sign test the required sample size used is 1007 i.e., n = 856 + 151 = 1007 which is greater than 25 (n 25). Hence the Test Statistic x = 151 can be converted to the Test Statistic as shown below (x + 0.5) ( ) z = n 2 2 (151 + 0.5) 2() z = 1007 2 On substitution we get, z = -22.18 From A-2 table, the critical values are z = -1.96 and z = 1.96 for two tailed test. Hence the critical region is (z -1.96)(z 1.96) From the above figure, we see that z = -22.18 does not fall within the critical region. Hence we reject the Null hypothesis and conclude that there is a sufficient evidence to claim that there is a difference between adults who know what Twitter is and those who do not know.