3. Wichita is about 3 times larger than Topeka. A poll of 300 voters was taken i

Question

3. Wichita is about 3 times larger than Topeka. A poll of 300 voters was taken in Topeka to find out whether or not residents favor building coal-fired power plants in Holcomb. The pollsters reported a margin of error of 6 percentage points. To have the same margin of error for the same poll in Wichita, approximately how large a sample should we take? a. 2700 b. 1800 c. 900 d. 300 4. To find out how Manhattan restaurant patrons feel about the ban on smoking in public places, a pollster plans to pass out a questionnaire to those at the Town Center Mall who would agree to answer the questions. What does it mean to say that there is undercoverage with this method of sampling? a. Those that do not wish to fill out the questionnaire could avoid the pollster. b. Those that do not go the Mall are excluded from consideration. c. Those that take the questionnaire could give false answers.

Explanation / Answer

we know that margin of error is given as

MOE = z*sd/sqrt(n)
given that moe = 0.06
z = 1.96 for 95% CI from the z table
n = 300

we caclulate sd as

sd = 0.06*sqrt(300)/1.96 = 0.5302

now wichita is 3 times bigger

so sd for wichita = 3*sd = 3*0.53= 1.59

0.06 = 1.96*1.59/sqrt(n)

sqrt(n) = 1.96*1.59/0.06

n = (1.96*1.59/0.06)^2

2697 approx

hence a

please note that we can answer only 1 question at a time , as per the answering guidelines

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