Question

A city ballot includes a local initiative that would legalize gambling. The issue is hotly​ contested, and two groups decide to conduct polls to predict the outcome. The local newspaper finds that 47​% of 2300 randomly selected voters plan to vote​ "yes," while a college Statistics class finds 46​% of 500 randomly selected voters in support. Both groups will create 99​% confidence intervals. Assume that all voters know how they intend to vote and that the initiative requires a major?

Answer 1

Answer:

A) 2.02 standard deviations from 600 - a win

B) The last interval was a close call.

Explanation:

n = 2300

p = 0.47,      q = 1-p = 0.53

μ = np = 1081

σ = √(npq) =  23.94

Z.025 = 1.96

B) Finding both confidence interval:

Confidence Interval = (μ-1.96(23.94)/√2300, μ+1.96(23.94)/√2300)

 = (1081 - 0.978, 1081 + 0.978)

= (1080.022, 1081.978)

(1080-600)/23.94 = 2.02 standard deviations from 600 - a win

B)

AS above

n=450, p=.54, q=.46

μ=np=243, σ=√(npq)=10.6

confidence interval (243-1.96(10.6)/√450 , 243+1.96(10.6)/√450)

= 243-.98, 243+.98) = (242.0, 243.98)

(244-225)/10.6=1.8 standard deviations from win