A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the riding.She has her assistants randomly sample 200 eligible voters in the riding by telephone and only 90 declare that they support her candidate.The observed z value for this problem is ___.
A)-4.33
B)4.33
C)0.45
D)-.31
E)2.33

Question

Quizplus · Accepted Answer

To calculate the observed z-value, we need to use the formula:
z = (p̂ - p) / sqrt [p(1-p)/n]
where p̂ is the sample proportion (90/200 = 0.45), p is the hypothesized proportion (0.60), and n is the sample size (200).

z = (0.45 - 0.60) / sqrt [0.60(1-0.60)/200] 
z = -4.33

Therefore, the observed z-value is -4.33, which corresponds to choice A.

A Political Scientist Wants to Prove That a Candidate Is