In a Harris poll adults were asked if they are in favor of a

In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the responses, 1271 answered \"no,\" 478 answered \"yes,\" and 357 had no opinion. What is the sample proportion of yes responses, and what notation is used to represent it?

Solution

Given no=1271, yes=478, had no opinion=357, n=2106. P=1/3, Q=1-P=1-.333=0.6667, p(yes responses)=478/2106=0.227. The table value at 5% level of significance is Ztab=1.96.

Ho:p=1/3 vs H1:p not=1/3, then |Zcal|=|(p-P)/[(PQ)/n]|=|-(0.227-0.333)/[(0.333*0.6667)/2106]|=|-0.106/0.0103|=10.3009>1.96, here |Zcal|>Ztab, so we reject null hypothesis, i.e., H1:p not=1/3 is accepted.