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 55​% of 500 randomly selected voters plan to vote​ "yes," while a college Statistics class finds 54​% of 1300 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 majority vote to pass. Complete parts a through c below. b.) find both confidence intervals c.) which group concludes that the outcome is too close to call? Why?

Answer 1

Question (b)

99% confidence interval for local newspaper

Given porportion of votes who plan to vote "yes" is 55% or 0.55

So = 0.55

n = 500

= 1- confidecne level

= 1- 0.99

= 0.01

/2 = 0.005

The z-score for which the area to its left is 0.995 will be Z/2

So Z/2 = 2.576 which has an area of 0.995 to its left

The 99% confidence interval for local newspaper = Z/2 * * (1-) / n

= 0.55 2.576 * 0.55 * 0.45 / 500

= 0.55 2.576 * 0.000495

= 0.55 2.576 * 0.022249

= 0.55 0.057312

= (0.4926888, 0.607312)

The 99% confidence interval for local newspaper is (0.4927, 0.6073) rounded to 4 decimals

99% confidence interval for College's Stastistics class

Given porportion of votes who plan to vote "yes" is 54% or 0.54

So = 0.54

n = 1300

= 1- confidecne level

= 1- 0.99

= 0.01

/2 = 0.005

The z-score for which the area to its left is 0.995 will be Z/2

So Z/2 = 2.576 which has an area of 0.995 to its left

The 99% confidence interval for Colleg's Statistics class = Z/2 * * (1-) / n

= 0.54 2.576 * 0.54 * 0.46 / 1300

= 0.55 2.576 * 0.000191

= 0.55 2.576 * 0.013823

   = 0.55 0.035608

= (0.504392, 0.575608)

The 99% confidence interval for College's statistics class is (0.5044, 0.5756) rounded to 4 decimals

Question (c)

The outcome is too close to call for the group that has a narrower confidence interval than the other

Here the 99% confidence interval for College's statistics class is narrower or lower than the 99% confidence interval for local newspaper

So the college's statistic class group concludes that the outcome is too close to call