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1. Suppose a pollster asks 1200 taxpayers in Kansas City, \"Do you favor raising

ID: 3071765 • Letter: 1

Question

1. Suppose a pollster asks 1200 taxpayers in Kansas City, "Do you favor raising taxes to pay for a new baseball stadium for the Royals?" What is the margin of error of the sample proportion if in fact 20% of the taxpayers in KC favor doing this? KC has a population size of about 450,000 2. Suppose a pollster would like to know the percentage of people in each of the fifty states who are optimistic about the economy in the coming year. The pollster would like to have a margin of error of about 3 percentage points in each state. What can we say about the sample sizes needed for each of the state polls (select the best answer)? a. The larger states should have the larger sample sizes. b. The states should have about the same sample sizes. c. To be accurate within 3 percentage points, the pollster would need to poll 3 percent of the population of each state

Explanation / Answer

1.

We first calculate the sample proportion denoted by p:

p = 20%

n = sample size

The margin of error of sample proportion is given by :

= ((p*(1 - p)/n) ^ (0.5) )* Z

= ( .2 * .8 / 1200 ) ^ 0.5 * Z

=  0.011547 Z

At 5% level of significance Z = 1.96 which gives

= 0.011547 * 1.96 = 2.2632%

Note here the population size would not be used as it is immaterial to our overall calculations.