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?

Question

Naomi Simon

Social Studies

20 July, 20:39

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?

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Answers (1)

Know the Answer?

Rigoberto Boyle · Answer 1

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