A campaign strategist wants to determine whether demographic

A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in Bowie County. Historically, around 62% of the county\'s registered voters have supported the Uniformians. In a survey of 196 registered voters, 57% indicated that they would vote for the Uniformians in the next election.

Assuming a confidence level of 95% and conducting a one-sided hypothesis test, which of the following should the strategist do?

A) Accept the hypothesis that the proportion of Uniformian voters has not changed.

B)Accept the hypothesis that the proportion of Uniformian voters has decreased.

C)Conclude that the proportion of Uniformian voters is now between 56% and 62%.

D) There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.

Solution

POPULATION PROPORTION Z TEST GIVEN P^          
          
Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.62
Ha:   p   >   0.62
As we see, the hypothesized po =   0.62      
As it is given,          
          
po =    0.62      
          
Getting the standard error of po, spo,          
          
spo = sqrt[po (1 - po) / n] =    0.03467046      
          
Getting the z statistic,          
p^ =    0.57      
z = (p^ - po)/spo =    -1.442149876      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.149260097      
significance level =    0.05      

Comparing p and the significance value, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is not enough evidence to support the hypotheses that the proportion of Uniformian voters has decreased. [ANSWER, OPTION D]