Only 12% of registered voters voted in the last election. Will voter participation decline for the upcoming election? Of the 330 randomly selected registered voters surveyed, 30 of them will vote in the upcoming election. What can be concluded at the α = 0.10 level of significance?

Answer:We are given that Only 12% of registered voters voted in the last election. We are supposed to find Will voter participation decline for the upcoming election?[tex]H_0: p = 0.12\\H_a: p \neq 0.12[/tex]Of the 330 randomly selected registered voters surveyed, 30 of them will vote in the upcoming electionn =  330 x = 30 We will use one sample proportion test   [tex]\widehat{p}=\frac{x}{n}[/tex][tex]\widehat{p}=\frac{30}{330}[/tex][tex]\widehat{p}=0.090[/tex]Formula of test statistic [tex]=\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]                                       [tex]=\frac{0.090-0.12}{\sqrt{\frac{0.12(1-0.12)}{100}}}[/tex]                                        =−0.923 Now refer the p value from the z table p value =0.1788 α =0.10 So, p value >  αSo, we are failed to reject null hypothesis So, voter participation will not decline for the upcoming election