A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state.She has her assistants randomly sample 200 eligible voters in the state 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

The observed proportion supporting the candidate is 90/200 = 0.45. The null hypothesis likely assumes the proportion supporting the candidate is 0.6 (or 60%). The standard error (SE) for a proportion is calculated using the formula SE = sqrt[p(1-p)/n], where p is the proportion under the null hypothesis, and n is the sample size. So, SE = sqrt[0.6*0.4/200] = sqrt[0.12/200] = sqrt[0.0006] = 0.02449. The z-value is calculated as (observed proportion - null hypothesis proportion) / SE = (0.45 - 0.6) / 0.02449 = -0.15 / 0.02449 ≈ -6.13. However, given the choices provided, the calculation seems to have been intended or interpreted differently, possibly due to a mistake in the calculation or a typo in the options. The correct approach to find the z-value involves using the formula mentioned, but none of the provided options exactly match the correct calculation. The closest option, based on the standard approach to calculating a z-value for a proportion, would be to expect a negative value since the observed proportion is less than the hypothesized proportion, which aligns with option A) -4.33 as the closest match, despite the discrepancy in calculation.

A Political Scientist Wants to Prove That a Candidate Is